Tottenham were deserved 3-0 winners at Wigan while Villa scored four goals in 12 second-half minutes for a 5-2 home win over Burnley.
Manchester City and Liverpool drew 0-0 to leave four teams chasing the final Champions League slot divided by one point.
Spurs have 46 points, ahead of Man City on goal difference. Liverpool and Villa are both on 45.
Chelsea are top on 61 points after their 2-0 win at Wolverhampton Wanderers on Saturday, taking full advantage of Manchester United's surprise 3-1 defeat at Everton which left the champions on 57.
Arsenal are third on 55 following their 2-0 home win over Sunderland.
The battle for fourth was to the fore on Sunday and Villa were first up at home to second-bottom Burnley.
The hosts trailed to an early Steven Fletcher goal before Ashley Young levelled after 32 minutes.
VILLA EXPLOSION
Villa then produced a spell of terrific attacking as two for Stewart Downing and one each for Emile Heskey and Gabriel Agbonlahor left Burnley reeling.
Villa, who face Manchester United in the League Cup final next Sunday, then eased off the gas but Martin Paterson's late score for the visitors was no consolation.
"That was pretty remarkable, really great stuff," Villa manager Martin O'Neill told Radio 5-Live.
"When you get good players playing with confidence and ability, there is nothing like it."
Tottenham, who beat Wigan 9-1 at White Hart Lane, looked likely to settle for a 1-0 win courtesy of Jermain Defoe's offside opener in a strength-sapping game on a muddy pitch.
Wigan keeper Chris Kirkland made two good saves and Luka Modric hit a post before out-of-favour striker Roman Pavluychenko came off the bench to score twice in the last six minutes.
How the fans at Eastlands would have welcomed such drama but instead they had to sit through one of the dullest games of the season as City and Liverpool seemed content to play for a draw from the start.
Even the introduction of Yossi Benayoun and Fernando Torres for the last quarter could not lift the torpor with barely a shot on goal from either side all afternoon.
In other games on Sunday Blackburn Rovers beat Bolton Wanderers 3-0 in a Lancashire snowstorm with goals by Nikola Kalinic, Jason Roberts and Gael Givet while a late free kick by Bobby Zamora gave Fulham a 2-1 home win over Birmingham City.
