The American then lost the 17th to go all-square and his poor putt on the last allowed Garcia to put Europe in front for the very first time.
Jason Dufner saw off Peter Hanson to make it 13-13 as the tension rocketed.
With two matches remaining on the course both teams sensed victory but it was Europe which held its nerve.
Martin Kaymer took a one-shot lead on the 17th and then held his nerve in impeccable fashion to hole the winning putt on the last and defeat Steve Stricker.
That left Europe on 14 points and Francesco Molinari secured the half needed to win the cup outright after finishing level with Tiger Woods.