Rooney set up one goal and scored another two minutes later Tuesday, putting United in strong position to reach the May 28 final at Wembley against Real Madrid or Barcelona. The second leg is next week at Old Trafford.
The 37-year-old Giggs became the oldest player to score in the competition, according to European soccer's governing body.
"An amazing man, his peak seems to have lasted so long," United manager Alex Ferguson said. "He doesn't show any sign of receding."
Ferguson lauded his team for a "fantastic performance" that he called one of the best in his 25 years as United's manager.
Giggs scored in the 67th minute off Rooney's pass. Rooney then struck in 69th minute after United had wasted a dozen chances against the unheralded German club.
"We have to say without envy that we never had a grip on the game except for the first 15 minutes," Schalke defender Christoph Metzelder said. "We were clearly outplayed."
Schalke goalkeeper Manuel Neuer made a string of fine saves to keep his team in the match for more than an hour despite strong pressure. Manchester United maintained possession nearly two-thirds of the game.
Rooney's performance came on the same field where he was infamously sent off during the 2006 World Cup in England's quarterfinal loss to Portugal.
"Schalke are a good team and we can't take them lightly," Rooney said. "We need to make sure we are professional and full concentrated."
Neuer, praised by his coach as one of the best 'keepers in the world, finally yielded a goal on a play orchestrated by Rooney. He held off three defenders and slipped a perfect pass to Giggs, who put the ball between Neuer's legs.
Two minutes later, Javier Hernandez ran unchallenged to the edge of the penalty area. He passed to Rooney, who drove a low shot past Neuer inside the near post.
"I think we showed too much respect from the start," said Neuer, whose team had knocked out defending champion Inter Milan in the quarterfinals. "We had trouble winning the ball and did not defend well."
United is seeking its fourth title in the competition; Schalke is in its first semifinal. Schalke had been unbeaten at home until the semifinal, while United still has yet to concede a goal away from home.
The Red Devils previously were eliminated four times against German opponents — in the semifinals against Borussia Dortmund (1997) and Bayer Leverkusen (2002) and twice against Bayern Munich in the quarterfinals (2001, 2010).
Schalke coach Ralf Rangnick understands what awaits in the next leg.
"We really have nothing to lose now," he said. "We won't give up."