The 76ers also snapped an eight-game losing streak at Bankers Life Fieldhouse that dated to April 2013.
"We were just over-thinking things", Simmons said. "We finally put it together".
Victor Oladipo scored a season high 36 points, including 24 in the first half.
Domantas Sabonis had 16 points and 11 rebounds. In between, Philadelphia struggled to maintain control.
The 76ers rebuilt a five-point lead early in the third quarter and Robert Covington scored eight of the Sixers' final 10 points in the quarter to give Philadelphia a 78-71 lead.
But when Shamet made back-to-back 3s and Dario Saric completed a four-point play 6:59 left, Philadelphia led 96-77 and the Pacers couldn't get closer than seven until the final seconds.
In other action, not even a season-high haul of 20 points from Australian guard Patty Mills was enough to prevent the San Antonio Spurs suffering a 95-88 loss to the Miami Heat.
While it's still not ideal that the team shot less than 32 percent from 3-point range, a trend that has plagued the team all season, by sharing the ball and giving everyone a chance to score, the Philadelphia 76ers found a way to win a must-win game.
Anthony Davis had 32 points, 15 rebounds and four blocks in his best game since spraining his right elbow almost two weeks ago as the New Orleans Pelicans ended a six-game skid with a 107-98 win over Chicago. Redick scored 10. Redick has scored in double figures in 21 consecutive games since March 26. If the Sixers can hold off the Pacers in the closing minutes, they'll get their first road victory of the season. IN is now 5-2 against the Eastern Conference and 3-1 against Atlantic Division opponents.
Dennis Schroder scored a season-high 28 points as the Oklahoma City Thunder extended their winning run to six with 95-86 away win against the Cleveland Cavaliers. IN was 12 of 17 from the free-throw line and 8 of 31 on 3-pointers. the only other player in double figures was Bojan Bogdanovic with 13.
And in the late games the LA Lakers edged Minnesota 114-110 while Toronto moved to an 11-1 season start with a 114-105 win over Sacramento.