On a day when Ryan Giggs won his first game in charge of Manchester United, Fulham had to settle for a draw against Hull City and West Bromwich Albion and Swansea City claimed crucial wins.
Aston Villa slipped deeper into trouble as they lost 4-1 to
Swansea at the Liberty Stadium in a match which featured a remarkable Shelvey goal from about 45 yards.
Swansea eased their own relegation fears with a win at Newcastle United last weekend and took the lead against Aston Villa after just 10 minutes as Wilfried Bony beat the offside trap to latch on to Shelvey's pass and calmly slot home for his 14th league goal of the season in all competitions.
Gabriel Agbonlahor turned in Marc Albrighton's excellent right-wing cross from just a couple of yards out to equalise in the 22nd minute, but Villa were back on level terms for just four minutes before Shelvey produced his moment of magic.
With a strike reminiscent of Rooney's goal against West Ham United last month, Shelvey controlled the ball on his chest just inside the centre circle and spotted Brad Guzan off his line before unleashing a dipping, swerving volley which flew into the top corner.
Pablo Hernandez's calm finish extended Swansea's lead in the 73rd minute and Bony added a late penalty after Nathan Baker had clattered into Marvin Emnes.
The result leaves Garry Monk's side on 39 points, while Villa are just four clear of the drop zone.
Huge setback
Everton's bid for Champions League qualification suffered a huge setback as they went down 2-0 at
Southampton to stay behind Arsenal, who can now move four points clear in fourth place with a win over Newcastle United on Monday.
Southampton produced an impressive performance but much of the damage was self-inflicted by Everton, with Antolin Alcaraz scoring an own goal inside the opening minute at St Mary's as he headed in a Rickie Lambert cross.
Seamus Coleman repeated Alcaraz's mistake in the 31st minute when Nathaniel Clyne swung over a cross from the right and he inadvertently nodded past Tim Howard, leaving Southampton firmly in control.
Everton battled back after the break and thought they should have had a penalty when Leon Osman went down in the box under a tackle from Dejan Lovren, but referee Michael Oliver felt it was a dive and yellow carded the midfielder.
Danny Rose had an eventful afternoon as he scored the only goal of the game at
Stoke to keep
Tottenham on course for a European spot.
Rose powered in a header on 33 minutes after Emmanuel Adebayor had cleverly skipped away from Glenn Whelan, poking the ball one side of his opponent and darting past him on the other before pulling back an accurate cross.
Stoke's chances of mounting a comeback were severely hit early in the second half when Ryan Shawcross was dismissed for a second bookable offence after a foul on Rose, which riled the Britannia Stadium crowd but looked a fair decision by referee Andre Marriner.
The Stoke fans booed Rose's every touch and he pushed Geoff Cameron in frustration after a foul to earn himself a booking before eventually being replaced, and Spurs had to withstand a late onslaught against 10 men to emerge triumphant.
