Sophomore Alphia Diallo (New York, N.Y.) also impressed in the win securing a double-double with 13 points and 11 rebounds.
Senior point guard Kyron Cartwright (Compton, Calif.) poured in 14 points to go with seven assists.
Cartwright also secured the game winning rebound as the Broncs' Stevie Jordan attempted a game tying three with less than 25 seconds to play but it hit the front rimmed and caromed into Cartwright's hands.
Rider red shirt freshman Joran Allen led all scorers with 28 points, including 21 in the second half.
The two sides each shot 46 percent from the field.
The Friars held a 41-31 lead after the first 20 minutes, but Rider came out on fire to begin the second half to jump right back in the contest.
An 8-2 run capped off by a Jordan three pointer cut Providence's lead to 43-39.
After a three pointer by senior Jalen Lindsay (Murfreesboro, Tenn.) pushed the Friars lead back up to eight, Broncs' forward Frederick Scott came back with an and one as well as a second chance basket to pull Rider within 53-50.
The Broncs took their first lead of the game since early in the first half on a three pointer by Jordan, but a Bullock and-one and a Makai Ashton-Langford (Worcester, Mass.) trey from the corner gave Providence the advantage back, 68-65 with 7:13 to play.
Rider, who came into the game average 84.5 points per game, refused to go away.
Allen finished a layup in transition to put the Broncs up 71-70.
When they needed it most, however, Bullock and Diallo were there to save the Friars.
Bullock drove base line for a basket plus a foul to put Providence back in front 73-71, and two free throws by Diallo increased the Friars edge to 76-71 with 3:25 left.
Down 79-71, Broncs red-shirt freshman Dimencio Vaughn swished a three pointer from the left wing but Maliek White (Richmond, Va.) and Cartwright hit free throws in the games waning moments to seal Providence's victory.
Cartwright got the Friars jumpstarted offensively with a pair of three pointers to give Providence an early 9-4 lead.
Leading 16-15 with a little over 10 minutes to go in the first half, the Friars went on a 19-6 run to gain some separation before the break.
Cartwright connected on an and-one jumper from the right elbow, Ashton-Langford went coast-to-coast, and Bullock drilled a three pointer to highlight the spurt and give the Friars a 35-21 advantage.
With less than 10 seconds to go in the opening stanza, Jordan hit a three from the top of the key to cut Providence's lead to 41-31 at the half.
Bullock led the Friars with 10 points, three rebounds, and two steals in the first half while Cartwright added nine points and dished out four assists.
Next up the Friars head to the Ryan Center on Saturday evening for a matchup with Rhode Island. Tipoff is scheduled for 5pm and the game will be televised on CBS Sports Network.
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