Parker had 15 points and a career playoff-high 18 assists, Duncan scored San Antonio's first six points of overtime and the Spurs bounced back after squandering a 13-point lead in the fourth quarter to beat the Memphis Grizzlies 93-89 on Tuesday night.
"I hate that we gave up that big of a lead in that situation," Duncan said. "But we were resilient enough to go to overtime and not let it affect us."
Duncan opened the extra period with a layup, and then made a tiebreaking putback on Parker's missed jumper. He then made a runner that bounced high of the back iron and rattled in for a 91-87 lead with 1:08 to play.
The Grizzlies had a chance to tie after Jerryd Bayless hit a jumper and Parker missed one of two free throws with 14.6 seconds left, but Bayless' 3-pointer from the left wing was off-target.
Memphis has fallen behind in all three playoff series so far, including rallying from an 0-2 deficit in the first round against the Los Angeles Clippers.
Game 3 is Saturday in Memphis.
"We're in the same boat we were when we left L.A. We're down 0-2. We've got to go home and take care of business at home," coach Lionel Hollins said. "It's not going to be easy, but that's where we are."
Bayless and Mike Conley each had 18 points to lead Memphis.
Duncan had 17 points and nine rebounds, missing most of the second half with foul trouble before coming up with the key baskets in overtime — even if it wasn't by design.
"It was just what was there more than anything," he said.
Memphis stormed back from a 13-point deficit with a 15-2 run over the final 8 minutes of regulation to tie it at 85 on Conley's runner in the lane with 18.2 seconds to play. The Grizzlies got the chance to pull even after Manu Ginobili was called for a flagrant foul for pulling down Tony Allen by his left arm on a fast-break layup try.
Allen hit both free throws and Memphis got possession, setting up Conley's tying basket at the end of a string of seven straight Grizzlies points.
But Memphis, which trailed by as much as 18 in the second half, could never pull ahead.
Up until the final stretch, Parker had been in control for 2 1/2 quarters.
Parker kept San Antonio humming along after Duncan went to the bench with four fouls, the last three picked up within a span of 30 seconds, early in the third quarter. Parker provided the assist on the Spurs' first seven baskets of the second half, and then scored the next two on mid-range jumpers before getting pulled for a rest with a 72-54 lead.
The Grizzlies mounted a 16-6 comeback while Parker was on the bench, getting as close as 78-70 after Zach Randolph scored inside following back-to-back Bayless jumpers.
Parker checked back in and soon had the lead growing again, ducking under Darrell Arthur to hit a floater and then knocking down a 3-pointer from the right wing to make it 83-70 with 8:14 to play. But then Parker finally went cold, missing five straight shots down the stretch as the Grizzlies rallied back.
He had 14 assists in the second and third quarters and went past his career-high for the regular season of 17 during overtime.
"He was unbelievable," Duncan said. "I know he's exhausted. We asked a lot of him. He was controlling the ball every time down the floor and he was making every right play there was.
"He was finding people, and people knocked down shots for him."
After Game 1, Memphis' guards outlined a game plan that involved picking up their defence earlier on Parker to keep him from getting into the lane and putting the Grizzlies into the scramble mode that allowed San Antonio to hit a franchise playoff record 14 3-pointers in the opener.
It wasn't until late that any of their plans started working.
"He's a Hall of Fame guard, people. He's been around, he's done great things in his career," Hollins said. "He just controlled the pace and got in the paint, found open guys. ... We battled him, though, and we wound up being in the game."
But then, Duncan — who missed a potential winning jumper from the left wing at the end of regulation — took over.
The Spurs put all five starters in double figures, getting 14 points from Tiago Splitter, 12 from Kawhi Leonard and 11 from Danny Green.
Randolph had 15 points and 18 rebounds after a two-point performance in Game 1, his lowest-scoring effort all season. Marc Gasol had 12 points and 14 rebounds.
Hollins talked before the game about wanting the Grizzlies — getting increased attention in their first Western Conference finals appearance — to avoid being like a boy in junior high school who suddenly decides he needs to change once he gets noticed by a pretty girl.
"We're who we are and we have to stay who we are, and we have to understand that no matter who's coming and talking to us, we have to be true to our identity," Hollins said, "and we can't go changing and shaving and taking a bath when we haven't taken one all along."
Memphis, with the league's best defence, looked like itself again early on while recovering from a 7-0 hole to turn it into a 15-13 slugfest after the first quarter. But after the Grizzlies went ahead for the first time, San Antonio surged back ahead with seven straight points. Just before halftime, the Spurs asserted control with a 13-0 run and went up 46-31 at the break.
Notes: There was a moment of silence before the game recognizing the deadly tornado that hit Moore, Okla., on Monday. ... The Grizzlies missed five shots on their next-to-last possession of the first half. Tony Allen's baseline drive was snuffed out by a Leonard block and he also missed the putback before Randolph missed two putback tries — one of them blocked by Duncan. Tony Wroten then missed the final follow shot. ... Parker's previous career best in the playoffs was 14 assists against Utah on May 22, 2007. Johnny Moore holds the franchise post-season record with 20 against Denver in 1983.