Quickfire Walcott earns Arsenal win at QPR
Walcott pounced in the late kick-off at Loftus Road in West London just moments after Gareth Bale, newly crowned English player of the year, had celebrated a spectacular winner as Spurs beat Southampton 1-0 in North London.
Bale cut inside from the right and held off a defender before firing home from 25 metres in the 86th minute against his former club.
At the bottom of the table, Wigan Athletic and Aston Villa also celebrated late victories to improve their chances of avoiding relegation to the Championship.
Callum McManaman scored in the 80th minute at the Hawthorns to give Wigan a 3-2 win over West Bromwich Albion after Roberto Martinez's team had twice fallen behind.
Villa left Carrow Road with a 2-1 triumph over Norwich City courtesy of Gabriel Agbonlahor's double, including the 89th-minute winner.
Second-placed Manchester City drew 0-0 at Swansea City on Saturday.
With Newcastle United drawing 0-0 at West Ham United, the relegation picture is also tight and unpredictable.
Just five points separate eight clubs between Wigan, in 18th place and the third relegation spot, and the Potters, who are 11th.
QPR and Reading, who beat Fulham 4-2 at Craven Cottage on Saturday, are already down.
The big winners in the relegation battle this weekend were Villa, who moved up to 13th place on 40 points, the tally traditionally considered the minimum required for survival in the Premier League.
Agbonlahor notched his fourth goal in as many games to give Villa manager Paul Lambert a triumphant return to former club Norwich, who are now 15th and just three points above the drop zone.
"Our effort after playing on Monday night [in a 6-1 victory over Sunderland] was outstanding," Lambert told the BBC.
"Agbonlahor has been playing excellently for us. He has the speed to hurt teams, and power as well.
"We have to keep going but it's another huge, huge win. This team is getting better and better every single game."
FA Cup finalists Wigan are aiming for another late-season escape, and their cause is helped by the fact they have a game in hand over their rivals.
"We showed our character and never accepted defeat," Martinez said. "To come back twice from behind at a place as difficult as this is huge.
"We have worked really hard for two months to get us in the position where, with two weeks of the season left, we are still involved in two competitions. If we stay up it would be like winning the title."
Newcastle felt they should have had three points at Upton Park after a Papiss Cisse effort midway through the first half was ruled not to have crossed the line.
Manager Alan Pardew said his side nonetheless responded well to media reports this week of a dressing-room split, which the club denied.
"The players needed to show a lot of what was said this week was complete rubbish, and we showed that," he told reporters.
"We had good spirit and unity and we should have had a goal. It was touch and go but it should have been given."
With his winner at White Hart Lane - in a game that was delayed for 30 minutes because of a traffic accident near the ground - Bale became the first Spurs player to score 20 league goals in a season since Jurgen Klinsmann in 1994/95.
"We got what we deserved for our play in the second half with a moment of individual brilliance in the split second that Southampton allowed Bale some space and he managed to put the ball in the back of the net," Spurs manager Andre Villas-Boas told reporters.
"Bale is in a moment of outstanding form, scoring goals out of nothing with great ability and really enjoying himself."
Bale's ex-Southampton youth team-mate Walcott also passed a personal milestone on Saturday - the first time he has scored 20 goals in all competitions in a senior season.
He received Mikel Arteta's pass and beat QPR keeper Robert Green in the first attack of the game, eclipsing Robin van Persie's 33-second effort for Manchester United against West Ham in November.
But Arsenal were indebted to keeper Wojciech Szczesny for preserving the three points as the Pole made an outstanding save from Loic Remy, diving low to his left with seven minutes remaining.
"Theo's finishing is better, he is stronger, and he is playing with more belief," Wenger told ESPN.
"He is 24 now... when players become more mature, and you can see that."