LOS ANGELES — Dirk Nowitzki scored 28 points and hit two go-ahead free throws with 19.5 seconds left before Pau Gasol and Kobe Bryant combined to commit a crucial turnover, and the Mavericks rallied for a 96-94 victory over the Lakers last night in Game 1 of their second-round playoff series.

Nowitzki had 14 rebounds for the Mavericks, who dramatically came back from a 16-point deficit in the second half of the perennial playoff teams’ first postseason meeting in 23 years.

Bryant scored 21 of his 36 points in the second half for the Lakers, but he fell down while trying to get the ball from Gasol with 5 seconds to play. After one free throw by Jason Kidd, Bryant missed a 3-pointer just before the buzzer.

Game 2 is tomorrow night at Staples Center.

Gasol had 15 points, 11 rebounds and seven assists for the second-seeded Lakers, who lost their second straight series opener. Their loss to New Orleans two weeks ago was much more surprising than this loss to the playoff-tested Mavs, but the Lakers’ lack of poise down the stretch should be scary to anybody anticipating a threepeat.

The Mavericks trailed 92-87 with 3:32 to play, but finished on a 9-2 run — showing all the late-game poise expected of Bryant and the two-time defending champions.

Lamar Odom scored 15 points for Los Angeles, which nursed a small lead throughout the second half until Nowitzki scored in the lane with 40 seconds left to trim the deficit to 94-93. After Jason Terry swiped the ball from Bryant, Gasol fouled Nowitzki on the Mavericks’ inbounds play, allowing the 7-footer to give Dallas its first lead since the second quarter.

Terry added 15 points for Dallas, which struggled on the boards.