They parred the next four holes as the tension mounted, but Westwood edged back in front on the 14th when a sensational second shot left him with a four-footer for birdie.
All his hard work seemed to be unraveling at the par-three 16th when his tee shot found deep rough and his hack out dribbled back down a slope, while Woods prowled the green eyeing a makeable birdie putt.
Woods’s effort finished agonizingly short and an ice-cool Westwood drilled in a long bogey putt that produced a roar as loud as if it were a birdie.
Pumped-up by his escape, Westwood launched a huge drive down the 17th and Woods panicked, sending his second shot into a bunker — a terrible miscalculation that resulted in a bogey six.
“If I hit it flat and flush, it’s fine, it carries, but I spun it and you spin it against that wind, it’s not going to go very far,” Woods said of the momentum-shifting moment.
Westwood sank his birdie putt to pull two clear and both parred the 18th.
The duo were put on the clock by the Royal and Ancient organizers, who punished Japan’s Hideki Matsuyama with a one-stroke penalty after he took too long on the 17th hole.
Matsuyama had birdied the ninth, 10th and 11th to move to one-under, but eventually slipped back to three-over.
Mickelson’s dream of a first Open title looked realistic as he got himself under-par, but three bogeys in his last six holes left him five shots behind Westwood and one ahead of Spain’s Sergio Garcia, who made hay early on with a 68.