CHAMPAIGN—Illinois needed something to feel good about after a rough stretch this month.There were the losses, one at Wisconsin that the Illini could stomach and another at unranked Penn State that was tougher to take.Then there was the rumor — quickly denied — that freshman Jereme Richmond wanted to transfer after missing practice and heading home before Saturday’s loss to the Badgers.All of this with No. 1 Ohio State headed to town Saturday.No. 23 Illinois found the answer to many of those problems Tuesday night, getting 20 points from Brandon Paul, 14 from Richmond and several late free throws that helped hold off 17th-ranked Michigan State, 71-62.The Illini (14-5, 4-3 Big Ten) led by as many as 10, at 53-43, on a 3-pointer by Paul with 13:08 to play.But they had to hold off a late Spartans charge that made Michigan State coach Tom Izzo feel as though his team was never more than a key shot or two from a potential win.One late possession neatly summed up the misery for Michigan State (12-6, 4-2).With the Spartans down 67-62 with just more than two minutes to play, Durrell Summers missed a jump shot that was followed by three straight missed chances to tip the ball in. Finally, Mike Davis swooped in to grab a rebound for Illinois and end the suspense.Paul scored 17 of his 20 points in the first half and was the biggest reason why the Illini hit 61.5 percent of their shots during the first 20 minutes.The Illini led 41-37 at halftime and outscored Michigan State 12-6 over the first seven minutes of the second half.They closed that stretch with two inside points from Richmond on a long pass from Demetri McCamey that sliced just over the outstretched hands of two Spartans defenders and a 3-pointer from Paul after Richmond forced a Michigan State turnover.But after a dunk that had revved up the home crowd, Kalin Lucas hit a 3-pointer that quieted fans and pulled the Spartans to 59-53 with 10:28 remaining. Lucas led the Spartans with 15 points.Just 46 seconds later, Delvon Roe sank a short basket that cut the Illini lead to 59-55. With 8:55 to play, Roe tipped in a miss to cut it to 59-57.The Illini, after riding their outside shooting much of the night, spent the next three minutes methodically rebuilding their lead at the free throw line.Mike Tisdale hit one, followed by two each from McCamey, Davis and Richmond to stretch Illinois’ edge back to 65-57.Davis finished with 11 points and 11 rebounds.Paul’s first-half outburst included nine points on 3-for-3 shooting from 3-point range.The sophomore guard, coming off the bench, hit one 3 that capped a 7-0 run that gave Illinois a 28-23 lead with 8:24 to play in the first half.Just under five minutes later he nailed his last 3-pointer of the half from the baseline in front of the Michigan State bench, giving the Illini a 38-31 cushion. Less than a minute later he added a three-point play when he was fouled by Keith Appling.