The Boilermakers (12-5, 2-2 Big Ten) trailed 33-29 at halftime, but they opened the second half with 10-5 run to regain the lead and held off the Illini (13-5, 2-3).
The 7-foot Hammons was a force inside for Purdue. He finished with a game-high eight rebounds -- the Boilermakers held a 42-31 advantage on the boards -- and was a big reason why Purdue scored 30 points in the paint.
The loss was the third straight for the Illini.
Rice played with a hip injury that led head coach John Groce to question earlier in the week if he would be able to play at all. Illinois stayed close through the second half but, fittingly, it was a bucket from Hammons that put the Boilermakers in control for good.
With 2:35 to play the Illini pulled back to within a point at 58-57 on a long, low-arc 3-pointer by Jon Ekey. The low shot looked like it might not fall, but when it did the crowd got loud and on its feet.
But at the other end, with Illinois playing tough defense, Hammons pulled down a Ronnie Johnson miss and calmly sank the short jumper for a 60-57 edge that, after the strong start to the half, would prove to be enough.
The final points of that early-second half run fell into the Boilermakers' laps in spite of coach Matt Painter's efforts to get Ronnie Johnson to slow the offense down.
"Hold up, Ronnie! Hold up!" Painter shouted at the guard.
Johnson didn't listen. Instead he quickly hit Basil Smotherman as he broke under the basket for a bucket that put the Boilermakers back on top, 39-38 and drew a "why not?" shrug from Painter. Purdue owned the boards in the second half, out-rebounding Illinois 23-7.
The Boilermakers led much of the first half, too. But as they headed down the tunnel at the State Farm Center at halftime, they had to wonder what has just happened.
With 3:52 left in the half, Purdue was up 27-19, its biggest lead of the night, and had just scored six straight points. The Illini didn't appear to have an answer.
But then Illinois started finding its range, thanks mainly to Abrams.
The junior guard sandwiched four straight jump shots around a 3-pointer from Kendrick Nunn to put Illinois back on top. Abrams' last dagger, a long 3 from way outside, put the Illini up 31-29 with 37 seconds before the half and they took a 4-point lead into intermission.
Purdue has won nine of the last 10 games with Illinois.
With the game Wednesday, the Boilermakers opened a stretch of three in seven days -- including Penn State at home Saturday and at Northwestern Tuesday -- that give the Boilermakers a chance to bounce back from a 1-2 Big Ten start.
After its 2-0 conference start the Illini have slumped toward the bottom of the Big Ten.