Woods moved in front on the 524-yard second hole with an eagle and, by the turn, was five up. The PGA winner completed the front nine at the 6,957-yard Poipu Bay Resort in five-under-par 31 while Love, who made it into the tournament as a replacement following the death of Payne Stewart, was at one-over 37.
Love birdied the 12th and 13th holes to cut Woods' lead to three, but it was not enough.
The previous day, Woods had to go deep into the back nine to defeat the Open champion, Scotland's Paul Lawrie, while Love, meanwhile, routed Masters champion Jose Maria Olazabal, 6 and 5.
Woods, who entered with $7,281,626 (pounds 4,467,000) in winnings this year, won another $400,000. He has won 10 of his last 14 tournaments.
The third-place match ended when Lawrie conceded to Olazabal after twisting his right ankle. He was walking from the ninth green to the 10th tee when he stumbled over some rocks. Olazabal was one-up at the time.
Lawrie was taken to hospital and the extent of his injury was not immediately known.
Two days after teaming up with Mark O'Meara to capture the World Cup in Malaysia, Woods had begun the defence of his Grand Slam title with the 4 and 2 victory over Lawrie.
Love left little to chance with a 29 on the front nine of his battle with Olazabal. "I played against a guy who was very hot today," Olazabal said. Love went one up with a birdie on the par-three third and never looked back.
"I grew up putting on Bermuda greens," Love said, "and I putted with confidence today." He also said he had been looking forward to playing match play. "I learned so much about match play from playing with Payne Stewart at the Ryder Cup," Love said. "Today, I could feel Payne was right there with me on every shot."
Woods struggled through a ragged front nine in his match with Lawrie, missing short putts on holes two, five, six and seven, and looking the worse for wear after flying all night from Japan to reach Kauai. After competing in the World Cup in Kuala Lumpur, Malaysia, he then played an exhibition match in Japan on Monday. "I wasn't feeling 100 per cent after flying in from Japan, and I didn't get a lot of sleep," Woods said. "When I started to wake up I started to play a lot better."
This is the third year in a row that Woods has competed in the Grand Slam at Poipu Bay, in 1997 as the Masters champion, in 1998 as first alternate when Mark O'Meara won both the Open and the Masters, and this year as US PGA champion.
"This course sets up well for me," the world No 1 said.
PGA Grand Slam of Golf matchplay tournament (Hawaii): T Woods (US) bt P Lawrie (GB) 4 & 2; D Love (US) bt J M Olazabal (Sp) 6 & 5.
Final: T Woods bt D Love 3 and 2. Third place: J M Olazabal (Sp) bt P Lawrie (Gbr) ret.Reuse content