Rosicky bags brace as Arsenal eye top-four
Aston Villa eased their relegation worries by winning 3-1 at Stoke City and Southampton virtually guaranteed their safety with a 2-0 victory at Reading who look doomed.
The day's other match between Norwich City and Swansea City ended in a 2-2 draw at Carrow Road.
Arsenal claimed their sixth win in seven league games despite having German centre-back Per Mertesacker sent off 19 minutes from time for a foul on Albion striker Shane Long.
James Morrison scored from the resulting penalty but Arsenal hung on for the three points that took them on to 56 points from 31 matches.
The race for third and fourth places looks to be between the three London rivals with Manchester United and Manchester City, who meet at Old Trafford on Monday, looking set to finish first and second.
Rosicky, who only started his first Premier League match of the season last week after months disrupted by injury, headed Arsenal in front after 20 minutes and scored from a rebound in the 50th minute.
Mertesacker was shown his red card by referee Howard Webb for tripping Long and after Morrison scored from the spot, Albion went close to an equaliser several times.
"Tomas Rosicky has been out for six months but showed his quality today and why he is so important to us," manager Arsene Wenger told Sky Sports.
"We know if we win all our games no-one can stop us, but it was a very nervy last 20 minutes. If you make a single mistake in the box it can cost you, but we kept our nerve."
Southampton dented the survival hopes of their former manager Nigel Adkins and his Reading team when they beat them 2-0 in a lunchtime kick-off.
Goals from Jay Rodriguez and Adam Lallana sealed Southampton's victory which lifted them to 11th. Reading stayed bottom of the table.
Aston Villa moved out of the relegation zone and improved their chances of staying up with a good win at Stoke, who are sliding towards trouble with just one victory in 13 league games.
Villa manager Paul Lambert told the BBC: "It was thoroughly deserved. We looked terrific from the off.
"I thought we defended really strongly and football-wise I thought we were excellent. Every time we went forward I thought we looked threatening."
He also praised young full-back Matt Lowton for a stunning goal that sealed the points.
"I don't think you will see a better goal in Europe let alone anywhere else than Matt Lowton's.
"The technique, chest control and volley was outstanding. He has played every minute of every game in the league and he has been outstanding."
Norwich seem to be consolidating their place in the Premier League and can look forward to a third season