Mitchell won the match with a drive-thru with 43 seconds remaining, but then appeared to slightly injure his leg from a foul in Paul Georges with 10 seconds to play. He made one of two free throws after limping to the line.
The goalie is the first Jazz player with at least 35 points in consecutive playoff games since Karl Malone in 1988.
Jordan Clarkson scored 24, including six at 3 points, while Joe English had 19 points and Rudy Gobert contributed 13 points and a career-high 20 rebounds in the playoffs.
Reggie Jackson led the Clippers with 29 points and George had 27. Kawhi Léonard scored 21 points but only managed two in the fourth quarter.
The series travels to Los Angeles on Saturday for Game 3.
Once the Clippers took their only lead at 101-99 after 3 straight points from Jackson, the Jazz forced nine straight misses to propel a 14-2 run that was capped by Ingles’ 3 point to reach 113 -103 with 3:07 to play.
In the second half, the Clippers shuffled multiple covers and cut passing lanes that typically garner Jazz’s own 3-point looks and Jackson got hot.
Mitchell scored 27 points in the first half – the most by a Utah player in the past 25 years – to give the Jazz an early lead, then a late second-quarter push to propel Utah to a lead 66-53 at halftime.
Mitchell shot 11 of 16 in the first half and did the same in the second half of the first game. He had 59 points on 22 of 32 shots during those four quarters.
Demonstrative Mitchell said he wanted to save energy with the exceptional physical demands of the playoffs, but he couldn’t help but show emotion during some of his spectacular finishes.
Mike Conley missed his second game after injuring his hamstring at the end of the Utah-Memphis series final, but the Jazz have now won six straight playoff games.
Jackson scored 16 points in the third quarter and the Jazz eventually started to miss shots against an active Clippers area. Their 21-point lead fell to four when Marcus Morris led the way and fired a tilt shot to make it 82-78. The Clippers made their comeback without Leonard, who spent most of the period with four fouls.
For most of the game, the Clippers searched for Gobert whenever they ventured into the lane and resorted to double push-ups and odd angles on the field goal shots that weren’t blocked by the French with long arms.
Leonard, George and Patrick Beverley were among the Clippers who followed Mitchell in addition to throwing doubles teams at the Utah goalie well over the 3-point line.
Instead of going small, the Clippers countered Gobert with DeMarcus Cousins and Ivica Zubac, who was hampered by foul issues in the first half.
Clippers: After posting the league’s all-time best free-throw percentage in the regular season (83.9%), the Clippers had 20 of 23. … Jackson’s 16 points in the third quarter were the most scored in a single quarterback in the playoffs. … LA beat Utah in the paint 42-32.
Jazz: Coach Quin Snyder and owner Ryan Smith presented Gobert with his third Defensive Player of the Year award before kick-off. … Ingles blatantly fouled Beverley for an arm to the head after the Clippers goalkeeper fouled him early in the fourth quarter. … The Jazz made 20 3-pointers (out of 39 attempts) to set a franchise record in the playoffs.