Bryant, the NBA's Most Valuable Player, scored just two points in the first half of the match before coming to life in the final two quarters, finishing with 27 points and nine assists, while Gasol added 19 points and seven rebounds.
"This is big for our team to come back from 20 [down] against the defending champs," Bryant told reporters.
"Once we got to within 10, we still had the energy to take the lead.
|"Once we got to within 10, we still had the energy to take the lead."|
LA Lakers guard
"I can get off any time and in the second half, I did that," added Bryant, who took only three shots in the first half.
San Antonio, defending NBA champions, squandered the chance to secure an important away win in the best-of-seven series, having just completed a game seven road victory over the New Orleans Hornets.
Tim Duncan led the way for the Spurs with 30 points and 18 rebounds.
"We had a great opportunity," Gregg Popovich, San Antonio coach, said.
"We didn't take advantage of it and it hurts like hell.
"We got to dig down deep, forget about this and figure out a way to come out just as aggressively as we did in the first three quarters."
The Spurs' stifling defence kept the Lakers at bay until mid-way through the third quarter, when Bryant took control of the match.
The Lakers guard hit a jump shot, found Gasol for a lay-up and then scored with a three-pointer to start a 14-0 run for LA, with Spurs held to 13 points in the final quarter.
"We were in pretty good shape," Tony Parker, who scored 18 points and grabbed 10 rebounds for Spurs, said.
"We had a great lead and had a great chance to win the game and we just didn't play well enough in the fourth quarter."
Game two is in Los Angeles on Friday.