1. February woes exaggerated
When it gets to February, it's often said that Arsenal traditionally struggle. But do they? While it's certainly true that the Gunners have had their fair share of woes in the second month of the year in recent seasons, almost all of those woes have come in the cup competitions.
Perhaps the main reason for the focus on February is the fact that Arsenal have gone out of the Champions League in the last 16 stage for five years in a row. There was a shock League Cup final defeat to Birmingham and an FA Cup home loss to Championship side Blackburn Rovers too.
But in the league, things really haven't been that bad at all. Okay, they started this February with a rather underwhelming 0-0 draw at home to Southampton. But the Gunners encountered Fraser Forster in top form on that evening and in the past five seasons, Arsenal's February fixtures in the Premier League have actually produced 14 wins, three draws and only two defeats. That's 45 points from 19 games. Title-challenging form, in other words.
Arsenal certainly couldn't afford to have an iffy February in the league this time around after ending January with two draws and a home loss to Chelsea, allowing Leicester and even Tottenham to steal a march on them in the race to be crowned champions.
In truth they weren't consistently brilliant against Bournemouth. They had only 49 per cent possession, a surprisingly low figure for Arsenal, even away from home. But they were able to take their foot off the gas and conserve energy for the big matches ahead after wrapping this game up midway through the first half thanks to two goals inside a minute. Not a bad way to end a three-match Premier League goal drought.
Tellingly, they took their chances when they came, something that Bournemouth failed to do. Arsenal had only 10 shots in this game but five of them were on target and two ended in goals. In contrast, the hosts had 17 shots but could put only four of them on target.
It's approaching the stage of the season where results are what really matter. The Gunners did what they had to do.
"We had a strong start, in the second half we had weak and strong periods but I don't think Bournemouth created many chances," Arsene Wenger said afterwards. "We had to win and we won."
2. Ramsey controlled the first half
That Arsenal took control of this game so early was largely down to Aaron Ramsey. The Welshman dominated midfield in the opening stages and played a key role in both goals.
Ramsey often looked for a chipped ball over the top to play in Olivier Giroud, Mesut Ozil or Alexis Sanchez. One such pass led to the first goal as Giroud nodded down his lofted pass and Mesut Ozil found the net. A minute later Ramsey provided the precise pass for Alex Oxlade-Chamberlain to make it 2-0 and effectively put the game beyond Bournemouth's reach.
Ramsey was comfortably the highest passer in the first half - he completed 43 of 47 passes, Ozil was the next highest with 30 completed passes. As Bournemouth started to dominate possession in the second half and Ramsey was moved to the flank in a tactical switch to allow Arsene Wenger to introduce Francis Coquelin for Alex Oxlade-Chamberlain, the midfielder actually completed only 11 passes after the interval - as well as missing a late chance when he might have squared the ball.
Andrew Surman (58) ended up as the game's overall top passer but the damage was done in the first half and Ramsey also topped the stats for ball recoveries (12) and tackles (5).
3. No assists, but a goal for impressive Ozil
While Bournemouth's Matt Ritchie had five shots and missed the target with all of them, Mesut Ozil needed just one shot in this game to make the difference.
Ozil is still waiting for his first Premier League assist of 2016, after teeing up 16 goals for others in the first half of the season. He created two chances in this game, taking his tally to 20 for 2016, but this time he was the man to find the net himself with a smart finish.
The German has scored in both of Arsenal's 2-0 wins over Bournemouth this season and was typically neat and tidy in possession in this game - particularly early on, when he didn't give the ball away once. By the end he had completed an impressive 52 of 56 passes and his tally of 22 in the final third was the highest of any player on the pitch.
"He's become a very important player and he's added a fighting attitude," Wenger said. "It was a top performance from him today."
4. Better sides could have punished Sanchez
Alexis Sanchez was starting his second Premier League match since his return from injury and while he did produce some bright moments, he is yet to reach top form.
The Chilean twice came close to scoring as his understanding with Ozil again threatened to pay dividends, but he was a little sloppy in possession on occasions - misplacing eight of his 49 passes.
Sanchez has never been renowned for his defending and his reluctance to track back did cause some issues, as Bournemouth full back Adam Smith was able to constantly raid unchallenged down the right. The Cherries switched play seven times during the game - Arsenal's didn't register one switch of play according to StatsZone - and Smith received a massive 40 passes, most of them in the Arsenal half.
It allowed the Bournemouth man to create three chances and have one shot. Ultimately it didn't lead to a goal, but Arsenal might not get away with it in quite the same fashion if Sanchez doesn't track back against Barcelona and their raiding right backs in the Champions League later this month. Don't worry lads, they only have Dani Alves and Aleix Vidal to choose from.
5. Gabriel kept Afobe quiet
The script seemed written for Benik Afobe to continue his fine form since joining Bournemouth by scoring against his old club, but it didn't happen.
Afobe worked tirelessly up front but didn't have a single shot during the match. That was in part down to a decent performance from Arsenal centre back Gabriel. The Brazilian has displaced Per Mertesacker in the Gunners starting line-up since Mertesacker was sent off against Chelsea, and his extra pace was certainly more suited to the task of keeping Afobe quiet.
Gabriel actually didn't make a single tackle during the match, probably because he was rarely in a position where he had to stretch to stop an attack. He did complete three interceptions as well as making two blocks and four clearances. Mertesacker may well have to wait a while to get his place back.
"I thought Benik played well but in the first half we didn't get enough bodies around him, he was quite isolated and that impacted on his ability to hurt them," Bournemouth boss Eddie Howe said afterwards. "We made a slow start to the game, which was totally against what we wanted. They dominated possession and we found it hard to get really good pressure on the ball.
"We reacted well and in the second half we dominated. We were looking for one goal to make a real game of it but it didn't come for us. Our pressure and possession didn't turn into chances."