Oladipo, who sank 11 of 19 shots overall, also contributed six rebounds, four assists and four steals.
The Pacers, who dominated most of the game, shot 45.6 percent while holding the Cavaliers to 38.5 percent.
The teams will play Game 2 on Wednesday night in Cleveland.
LeBron James contributed a triple-double for the Cavaliers with 24 points on 7-of-17 shooting, 12 assists and 10 rebounds. JR Smith scored 15 points off the bench, and Kevin Love had nine points and team-high 17 rebounds for Cleveland.
Pacers center Myles Turner scored 16 points on 6-of-9 shooting. Forward Bojan Bogdanovic struggled with his shot, hitting 5 of 17, but he had 15 points. Lance Stephenson scored 12 off the bench for Indiana.
Trailing 69-50 in the third quarter, Cleveland used a 13-1 run, capped by Love's deep 3-pointer, to trim the deficit to 70-63. The Pacers, who led by as many as 23 in the quarter, had to settle for a 73-65 advantage after three quarters.
After the Cavaliers closed the margin to 76-69 with a driving layup by James, the Pacers answered with a 12-2 run, including 3-pointers by Oladipo and Bogdanovic, to take 88-71 lead with 7:28 to go in the fourth quarter.
James-led teams had won 21 consecutive first-round games with the Miami Heat and Cavaliers. The Cavaliers swept the Pacers in last year's first round.
Oladipo scored 16 in the first half to lead the Pacers to a 55-38 edge at the break. Turner sank a 3-pointer with 1.2 seconds left to provide the halftime margin. The Cavaliers had trimmed the Pacers' 21-point lead to 42-32 in the second quarter before Indiana closed the half strong.
The Pacers shot 47.6 percent in the first half compared with 36.6 percent for the Cavaliers. The Pacers were 7 of 14 from the 3-point arc while the Cavs were 2 of 14.
Overall, Indiana made 11 of 28 3-point attempts while Cleveland hit 8 of 34 from long range.
The Pacers won the regular-season series 3-1.
--Field Level Media
Indiana | Cleveland | |
Victor Oladipo 32 | Scoring | LeBron James 24 |
Darren Collison 6 | Assists | LeBron James 12 |
Myles Turner 8 | Rebounds | Kevin Love 17 |
Bojan Bogdanovic 4 | Free Throws Made | LeBron James 10 |
Victor Oladipo 4 | Steals | Larry Nance Jr. 2 |
Victor Oladipo 1 | Blocks | Jeff Green 1 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Indiana | 98 | 45.6 | 11-28 | 15-25 | 19 | 44 | 4 | 12 | 11 |
Cleveland | 80 | 38.5 | 8-34 | 12-20 | 21 | 46 | 4 | 7 | 17 |