Woods scored just before the break to put Tigers ahead for the first time in the game, following up breaks by Ayoola Erinle and Sam Vesty to charge through Gordon D’Arcy and Isa Nacewa and score by the right of the posts. Scrum-half Julien Dupuy added the conversion.
Dupuy also kicked two penalties as Leinster finished the half down to 14 men with tighthead Stan Wright given a yellow card for tackling Vesty off the ball.
Leinster had twice taken the lead, first through Brian O’Driscoll’s early drop goal and a brilliant effort from Johnny Sexton, who dropped at goal from just inside the Tigers half. Sexton also kicked a penalty for Leinster, who had lead 9-3 after 20 minutes.
Head coach Richard Cockerill recalled Alesana Tuilagi, who was available after suspension, and the fit again Martin Castrogiovanni. They were the only two changes to the side that started the Guinness Premiership Final at Twickenham, with Johne Murphy and Julian White named among the replacements this Saturday.
Leinster made one change to the side that beat Munster in the semi-final with Jonathan Sexton partnering Chris Whitaker at half-back after injury to Argentina fly-half Felipe Contepomi. Former Tigers lock Leo Cullen captained Leinster and was joined in the forward pack by Shane Jennings, who also spent two years at Welford Road before returning to Ireland.