Henton posted a double-double with 21 points and 17 rebounds for the Friars (7-2). Batts overcame a Rams double-team to shoot 8 for 19 and finish with 23 points.
"I thought Kadeem and LaDontae were the best two players on the floor tonight," said Providence coach Ed Cooley. "Between their size and girth and athleticism . I really appreciate these two horses."
After trailing 27-26 at halftime, the Rams (2-7) allowed two Friars runs in the second half that put the game out of reach. One minute into the second, Henton scored six points on an eight-point Providence run for a 41-33 lead. The Rams cut the deficit to three points, only to allow 10 consecutive points over the course of 4 1/2 minutes in the middle of the half.
Cooley said Henton played his "best collegiate game."
Providence dominated on the glass, grabbing 41 rebounds to Rhode Island's 28. The Friars' 14 offensive rebounds doubled the Rams' seven.
"I just tried to play hard and get to the board," Henton said.
But Providence performed on defense as well, shutting down Rhode Island's outside shooting to allow only three treys in 18 attempts.
Rhode Island coach Dan Hurley expressed particular disappointment that Providence was able to disrupt his team's ability to hold onto the ball.
"We've been one of the best teams in the country in terms of not turning the ball over," Hurley said. "It's disappointing to turn the ball over 20 times to a team playing a zone."
The Friars, who have been playing with only six scholarship athletes due to injury and ineligibility, had to contend with Bryce Cotton's jammed knee. Cotton, who has averaged 22.1 points per game this season, played 39 minutes and scored 11 points.
"Cotton did an unbelievable job," said Cooley. "He dealt with a lot of pain today."
Between Cotton's impairment and Vincent Council's hamstring injury that has kept him off the court for the past several weeks, the Friars were missing their two strongest offensive presences.
"Our players have done an unbelievable job," Cooley said. He added that if someone had told him the day Council was injured that his team would be 7-2, he would have "asked to have a sip of what he was drinking."
Several early Rams fouls brought the Friars to the bonus only 8 minutes into the second half. Providence capitalized going 18 for 19 on free throws.
In the first half, the Friars made 35.7 percent (10 of 28) of their shots. Providence brought the ratio up to 44.8 percent (13 of 29) in the second half, shooting 70 percent over the first 7 minutes. The Friars' final 40.4 percent (23 of 57) topped the Rams' 38.5 percent (20 of 52).
Providence set the pace throughout the opening half, only ceding the lead twice for about 1 minute overall. Batts' 10 points and four rebounds carried the Friars in the first 20 minutes.
Cooley praised Hare after the game, calling the freshman "a special, special player."
Mississippi State freshman guard Malik Newman will withdraw from the NBA draft, but sources told ESPN he might explore other opportunities besides returning to Mississippi State.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.