Love has 21 career victories, three in Greensboro. His previous two wins came across town at Forest Oaks Country Club in 1992 and 2006, and he had just one win since then - at the 2008 Children's Miracle Network Classic in Florida.
Love finished at 17-under 263.
Gore, the third-round leader, shot a 69. Scott Brown (68), Charl Schwartzel (66) and Paul Casey (67) were two strokes behind Love.
Love, who was four strokes back after three rounds, started strong with four birdies and an eagle on Nos. 2-6. He moved to 17 under with an eagle on the par-5 15th - the first of his career during a competitive round on that hole.
He closed with three straight pars, walked off the 18th green with a two-stroke lead over Brown and Gore, and headed to the range to rest for a possible playoff.
Brown pulled within one stroke of Love with a birdie on 15, and Gore made things even more interesting with an eagle on that hole.
Neither got any closer.
Brown hit his approach on the 18th to about 60 feet, left his putt about 10 feet short and three-putted for bogey. Gore needed to make a 50-foot birdie putt on 18 to force a playoff, but he left it about a foot short to wrap up the victory for Love.
There was quite a crowd near the top of the leaderboard for a while. Midway through the afternoon, five players shared the lead at 15 under.
None of them was Woods.
Chasing his first victory since 2013, he opened with six straight pars, including one on the easiest hole on the course - the par-5 fifth, which he birdied in each of the first three rounds.
Woods sent his tee shot on the par-3 seventh into the huge gallery that had been waiting for him to reel off some birdies and make his move, then two-putted for his first bogey.
And when he made the turn, he was three strokes behind co-leaders Gore and Brown - his playing partner.
Brown, who had a hole-in-one on the par-3 third, joined Love at 17 under with a birdie on 11 - the same hole that pretty much sank Woods.
Woods' chip-and-run on the 11th ran all the way off the green. He couldn't keep his ensuing chip on the green and wound up three-putting for triple bogey. Not even three straight birdies on Nos. 13-15 could help him recover.
Woods was far from the only player who needed to play well at Sedgefield to advance to next week. Defending champion Camilo Villegas finished at 10 under - good enough to move him from No. 129 to No. 123 and put him in The Barclays.
But Scott Langley, who arrived at No. 126 on the points list, dropped a spot after bogeys on four of his final six holes.
-AP
