Woods -- a controversial captain's pick by Fred Couples -- paid dividends in Sunday's match with the United States seeking one point to retain the cup.
The highlight was Woods' spectacular bunker shot into concession range at the par-five 15th.
After surrendering that birdie, Baddeley missed a chip from the back of the green, handing Woods the point and giving the Americans their fourth consecutive Presidents Cup.
Woods clinched the prize for the second straight time. He bested Y.E. Yang two years ago at Harding Park for a U.S. win.
"We played really well today," Woods said in a televised interview. "I played well all week. I didn't make putts. Today was a different deal. For some reason, I felt it."
The final margin was 19-15 for the Americans as the two sides split Sunday's 12 singles matches.