Robin van Persie's penalty kick gave Manchester United a 2-1 victory over 10-man Liverpool on Sunday, settling a heated Premier League meeting between the fierce rivals after emotional tributes were paid to the Hillsborough disaster victims.
Van Persie beat Liverpool goalkeeper Pepe Reina in the 81st minute after Antonio Valencia was fouled by Glen Johnson to secure United's first win at Anfield since December 2007.
"Over the last three or four years we've come here and played a lot better and not got anything - that's how it goes sometimes," Giggs told Sky Sports television. "It's always tough against a team like Liverpool who keep the ball well. Even if they go down to 10 men they don't change, they keep the ball, and that's always tough."
Liverpool played with 10 men for more than 50 minutes after Jonjo Shelvey's sending-off before half time but still managed to take the lead through Steven Gerrard's volley within a minute of the second half starting.
Defender Rafael da Silva equalized five minutes later, curling the ball past Reina, and Van Persie's winner ensured second-place United prolonged winless Liverpool's worst start to a season in more than 100 years.
The build-up to the match, though, had been about the fallout from the report into the 1989 Hillsborough tragedy that absolved Liverpool supporters of any responsibility and exposed a police cover-up.
Old rivalries between Liverpool and United were put aside before the first match at Anfield since the report was published, with both sets of players emerging on the pitch wearing tracksuit tops featuring the number 96, the number of Reds fans crushed to death 23 years ago.
Liverpool striker Luis Suarez and United defender Patrick Evra ensured a reconciliatory start as they joined the other players in a pre-match handshake. Last season Suarez refused to shake Evra's hand when the teams played at Old Trafford after the Uruguay international was banned for racially abusing his United rival.
For the first minute of the match three sides of Anfield displayed mosaics featuring "The Truth," ''Justice" and "96."
The tributes seemed to inspire Liverpool's players on the pitch, with domination from the hosts.
Once Giggs had flashed an early shot wide the momentum was all with Liverpool as Suarez's cross-shot was stopped by Anders Lindegaard and headed away by Jonny Evans under pressure from Fabio Borini.
Gerrard drove a low effort from Shelvey's corner into the side-netting and Suarez looped a right-footed shot wide before the usuual hostilities in the north-west derby ignited.
Shelvey robbed Giggs in midfield but as the ball broke free he launched himself at Evans and the inevitable outcome was a red card.
Even with a numerical disadvantage Liverpool continued to pressure United and Suarez drew Lindegaard into a low save from his free kick.
And at the start of the second half, substitute Suso saw his cross half-cleared to Johnson. A tackle from Paul Scholes, on for Nani at half time, succeeded only in diverting the ball toward Gerrard, who volleyed home left-footed in front of the Kop.
The Reds captain, whose 10-year-old cousin Jon-Paul Gilhooley was the youngest victim at Hillsborough, whirled away pointing both arms to the sky in celebration and remembrance.
The lead was short-lived, however, and within five minutes United were level when Shinji Kagawa laid the ball off for Rafael to brilliantly curl left-footed over Reina and in off the far post.
But, even with a man down, Liverpool pushed for a winner with Suso having a shot tipped over by Lindegaard and Suarez continuing to trouble the United defense.
As the match entered the final 20 minutes United began to take more control though, and the winner came from Liverpool giving away possession on the halfway line.
Daniel Agger and Johnson collided to allow Valencia to race 50 yards into the area and, although Johnson got back, he could only bring down the Ecuador winger. Van Persie drilled home despite Reina diving the right way and getting a hand to the ball.