Giggs' corner from the United right-hand side was inadvertently flicked on at the near post by Jordan Henderson and into the path of Rooney, who volleyed beyond Reina from close range to open the scoring.
Jay Spearing was then hounded down by Valencia around the edge of his own penalty area, allowing the Ecuadorian to roll a pass into the path of Rooney, who steered the ball into the back of the net to leave Liverpool reeling.
United were looking comfortable until an innocuous free-kick into the penalty area was mis-controlled by Rio Ferdinand, allowing Suarez to bring the away team back into the game from inside the six-yard box.
United were able to hold on to ensure that the Reds continue to trail Chelsea, Newcastle and Arsenal in the race for a place in next season's Champions League.
Everton gained their second 'top-four' scalp in two games at Goodison Park, beating Chelsea 2-0 in the Premier League on Saturday.
David Moyes' men opened the scoring just five minutes in courtesy of Steven Pienaar's wonderfully controlled strike, with the South African making his return from a loan stint at Tottenham.
A brilliant run in off the right from Donovan found the Blues' defence backpedalling, and the American's weighted pass allowed striker Stracqualursi to fire on target and seal a valuable three points.
Wigan secured just their fourth win of the season with a battling 2-1 victory over Bolton to close the gap at the bottom of the table.
Gary Caldwell gave Wigan the lead in the 43rd minute at Reebok Stadium but the hosts equalised through a wonder strike from Mark Davies just after the hour mark.
A James McArthur tap-in with 14 minutes to go won the game for the visitors and secured bragging rights over their local rivals.
Norwich City held on for a vital 3-2 away win over Swansea City in the Premier League on Saturday.
Swansea took the lead in the 22nd minute through Danny Graham's first goal of the match, after a superb cross from Nathan Dyer.
Norwich scored three times in the opening 17 minutes through Anthony Pilkington and Holt twice
Graham's late penalty ensure for a thrilling finish, the Welsh side slipped to a disappointing defeat to their fellow promoted club.
A sublime first-half display proved enough for Blackburn as they secured an important 3-2 win against QPR at Ewood Park.
Strikes from Yakubu and Steven N'Zonzi gave the hosts the early ascendancy before a Nedum Onuoha own-goal made it 3-0 at half-time.
Substitute Jamie Mackie netted a second-half brace to set up a nervy finale but Steve Kean's men held on to their lead to draw level on points with QPR and Wolves in the Premier League table.
Arsenal's Thierry Henry signed off from the Premier League in fairytale fashion with a late winner in a 2-1 win over Sunderland on Saturday.
James McClean put Sunderland ahead in fortunate circumstances, but substitute Aaron Ramsey equalised before Henry struck a dramatic winner.
Pavel Pogrebnyak scored on debut to help Fulham to a 2-1 Premier League victory over Stoke City on Saturday.
Pogrebnyak opened his account in English football with a thumping finish after nearly 15 minutes at Craven Cottage, before Clint Dempsey's swerving shot hit the bar and rebounded off Thomas Sorensen into the net for a 2-0 lead.
The visitors slipped to a fourth consecutive defeat in spite of a late goal from Ryan Shawcross.
Four assists from Emmanuel Adebayor propelled Tottenham to a 5-0 victory over Newcastle.
Adebayor low cross found its way beyond Tim Krul to the onrushing Assou-Ekotto to slide into an empty net.
Two minutes later Adebayor again got the better of Fabricio Coloccini and sent a superb teasing cross across the box from the right touchline. Arriving right on cue was Saha to superbly tuck away his first goal for the club, leaving Krul no chance from six yards.
The Togolese striker, not content with a brace of assists, cushioned the ball into Saha's path for the Frenchman to double his tally and move Spurs into a commanding position.
Bale's low pass found Adebayor who saw his shot saved by the legs of Krul. The rebound though, dropped to the on-rushing Kranjcar to slot past Krul and into the net.
Assou-Ekotto's deep cross was headed back across the box by Saha to the unplayable Adebayor to volley the ball past Krul.
