The tandem started the day in a tie for 15th, but shot a 4-under 68 in the final round to finish at 23 under overall.
Woods had his worst round of the tournament, firing a 3-over 75 to finish tied for 15th at 8-under 278, nine strokes behind winner Phil Mickelson.
"I didn't hit it as bad as the score indicated, but I putted awful," Woods said. "As good as I felt on the greens yesterday, I felt bad today. Anything I tried to do wasn't working. Consequently, I made a ton of mistakes on the green."
"Tiger is close," Romo said. "He's building something; it's only a matter of time."
ESPN The Magazine's Sarah Turcotte and The Associated Press contributed to this report.