Garcia, who began the day leading by two, carded a 3-under-par 69 to move to 18-under for the tournament. Woods went two shots lower than his 20-year-old counterpart on Saturday, thanks largely to a quick start.
What was a three-man race as the day began has dwindled to a possible one-on-one Sunday showdown. Playing in the final group with Garcia, Davis Love III bogeyed two of his first four holes in the third round and never truly recovered. Love struggled to a 1-under-par 71 to fall from two shots off the lead as play started to four back by day's end.
Love will play in the penultimate pairing on Sunday with good friend Fred Couples, who is a full ten shots off the lead at 8-under-par.
Woods caught Garcia early in the third round by birdying four of his first seven holes. A bogey at the 10th dropped Tiger one off the lead, a lead that was quickly extended to two shots when Garcia birdied the 11th.
Tiger and Sergio each posted a pair of birdies at the 14th and 16th holes, however, the Spaniard also birdied the 17th to move three strokes clear of the world's No. 1-ranked player.
Entering the home hole at 20-under, Garcia hit his approach shot on the par-4 446-yard layout into the lake in front of the green. The resultant double-bogey was the lone blemish on Garcia's Saturday scorecard.
'Knowing Tiger is behind you, you want to have as big advantage as possible,' said Garcia, who added: 'I've never played with Tiger on Sunday.'
Garcia defeated Woods in August in another unofficial event, the made-for-television 'Battle at Bighorn' match-play. Garcia earned $1.1 million for that victory. Should he collect a second win over Woods, he'll pick up another $1 million.