Tim Duncan gave the Suns a chance by missing three of four free throws in the final moments, including a pair with 5.1 seconds to go.
The Suns grabbed the rebound and got the ball in the hands of Marbury, who raced up court. With the clock running down, he pulled up for a runner from just outside the three-point line at the top of the key that caromed off the backboard.
The officials counted the basket after briefly reviewing replays. There was no argument from the Spurs.
"That shot was a teardrop from God," Marbury said. "Things were getting tough, but I didn't stop shooting. We never gave up, we never got ourselves into a situation where we'd panic."
"We were in the game, but they did a good job of staying with us," Duncan added. "We just didn't hit our shots from the free-throw line."
Marbury scored 26 points and Shawn Marion added 24 and 12 rebounds for the Suns, who showed their success against San Antonio in the regular season was no fluke. Phoenix won three of the four meetings, including one here.
Suns Coach Frank Johnson admitted his team was extremely fortunate to come away with the victory.
"Yes, we're excited to come in and steal a game and that's what I call it, stealing a game," Johnson said. "You have to be in position to steal a game. We were fortunate to steal."
The Spurs were nearly unbeatable in the second half of the season, winning 41 of their last 50 games. But it took just one game for them to lose home-court advantage.
Poor foul shooting was the Achilles' heel for the Spurs during the season, and it hurt them in this one as well. San Antonio made just 26 of 41 free throws.
"Our two nemeses this year are free throws and turnovers," Spurs Coach Gregg Popovich said. "In all our losses, either one or both of those were the reason we lost."
Stephen Jackson had 23 points to lead the Spurs, who opened a 12-point lead late in the third quarter but could not shake the Suns.
Game 2 will be Monday night in San Antonio.
"We never stopped fighting," Phoenix guard Penny Hardaway said. "They missed important free throws down the stretch and we capitalized. This win was huge for us and it definitely gives us the momentum."
The Suns grabbed their first lead since early in the first quarter at 80-79 on Marbury's jumper with two minutes left in regulation. Duncan's dunk and two free throws by Jackson gave the Spurs an 83-80 lead with 1:19 to go.
Jackson hit two more from the line to make it 87-87 with 16 seconds left, but Amare Stoudemire banked in a 3-pointer from the top of the key with 7.9 seconds remaining to force overtime.
"I saw Marbury getting double-teammed, so I just knew I had to take that shot," said Stoudemire, who also scored 24 points. "They didn't expect me to step back and take the three. It was a shot that I have confidence in. As a team, we know what it takes to win."
David Robinson scored 18 points for the Spurs, two shy of his season high, including a dunk that gave San Antonio a 93-91 lead with 1:08 left in overtime.
Duncan, who finished with 17 points and 13 rebounds, kept it a one-possession game by converting just one of two from the line with 16 seconds to go. The Suns closed within 94-93 on Marbury's layup with seven seconds remaining.
After San Antonio's Tony Parker missed the second of two foul shots a second later, Duncan grabbed a huge offensive rebound but could not convert from the line.
"They made two great plays down the stretch," said Duncan, referring to Stoudemire's three-pointer and Marbury's game-winner.
"You have to want to take that shot and you have to know that you are going to make it," added Marbury, who was just nine of 28 from the field. "You dream about that shot and practice it hundreds of times when you are a kid growing up."
The Spurs shot just 40 percent from the field and made only five of 24 three-pointers.