Schweinsteiger, who hit two goals in Germany's 2006 World Cup third-placed play-off success over the Portuguese, struck after 22 minutes -- and Miroslav Klose added a second four minutes later.
Jay Bothroyd hit the first of his two goals on two minutes, slamming home after Michael Chopra's shot was saved.
Andrew Martin notched a hat-trick on the opening night of the season against Cardiff at the Odyssey Arena while Robins hit the Giants' other two goals.
Lewes then hit back to astonishingly level with two goals in five minutes from Aaron Hopkinson and Louis Pople.
Burnley's first-half composure had disappeared and Spurs hit the Clarets again with two more goals inside three minutes to seal the victory - and almost certainly a place in a second successive final.
Leading 2-1 from the first leg Roma went 1-0 down early on but hit back with three goals, two from Mattia Destro and one from Vasilis Torosidis before Ricardo Alvarez grabbed a consolation for Inter.
The latter match at Goodison Park saw the Toffees hit back to draw 3-3 with two goals in injury time.
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Only Spice's expertly timed tackle denied Malone a breakaway try, and he also tried his luck with two drop goals, one of which hit the post while the other was well off-target.
Ireland, who has scored match-winning goals in his last two games and has hit three in his last three appearances, is looking to the fans to give the players the lift they need against Slovakia.
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Kilmarnock trailed to Mark Kerr's first half strike but hit back through goals from Liam Kelly and Kevin Kyle to boost their survival hopes and establish a two-point lead over Falkirk.
The visitors had been two goals ahead inside 12 minutes as Van Persie's early shot rebounded off a post to hit David Luiz and dribble over the line.
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