The English duo dominated from start to finish, taking the lead on the second hole.
Woods looked way below his best, and it was his missed putt on the sixth green that saw Europe go two up.
He made up for it by setting Stricker up for a tap-in at the eighth with a superbly struck shot, reducing the deficit to one.
Poulter restored Europe's two-hole advantage with a superb chip in from the greenside bunker at the 12th following a poor approach from Rose.
Woods then compounded his wretched day by missing a short putt at 12, allowing Poulter to roll in for a three-up lead.
The world number two did find the cup for a par at 13, which cut the lead back to two.
However, Europe bounced back once with a well-holed putt from Poulter at the 14th, only to give one straight back at the next hole.
It was proving to be a bumpy ride, with both teams nipping holes off each other until Poulter teed up at the 17th, knocking an iron safely onto the fringe.
Woods also hit the green, but he had left Stricker with a trek across the dancefloor. Stricker could not find the cup and Rose chipped to within inches for a 2&1 victory.