Villegas has never had a 54-hole lead in his three years on Tour.
The 26-year-old Colombian was tied with Jim Furyk when the third round was suspended Saturday evening by darkness, with Furyk already done with a 66.
Villegas saved par from a bunker with a 15-foot putt on No. 5, missing a 10-foot birdie putt at No. 7, then took the outright lead with his birdie on the par-5 eighth. He was at 13-under 197 and will play in the final group Sunday afternoon with Furyk and Anthony Kim, who also completed a 66 in the morning.
Kim was at 201 with Tim Clark (66) and Brian Gay, who was challenging for the lead as he finished his third round until a three-putt from 12 feet for a double bogey on No. 8. He wound up with a 67.
Phil Mickelson played one shot more than he had hoped in the morning. Lefty was at 7 under and faced a 20-foot birdie putt on No. 8, but he three-putted for bogey and had to settle for a 71 that left him seven shots behind.
A victory by Villegas might be enough for Vijay Singh, who won the first two playoff events, to clinch the FedEx Cup and the $10 million prize without even having to play in the Tour Championship.
This is the second straight week that Villegas has been in contention. Last week at the Deutsche Bank Championship, he was one shot behind Mike Weir going into the final round at TPC Boston, only for Singh to close with a 63 to win by five shots.
Furyk will be going for his first victory of the year, giving himself a chance with a 62-66 on Saturday as some players went 36 holes to get the weather-plagued tournament back on schedule.
Rain prevented the BMW Championship from starting until Friday, and a 90-minute fog delay Saturday morning kept Villegas and 22 other players from finishing the third round.