For the first 20 minutes Monday against DePaul, Georgetown hardly resembled the team that upset then-No. 7 Michigan State on Saturday. That changed when the Hoyas regrouped and the Blue Demons came apart in the second half. Georgetown scored 23 points off 13 DePaul turnovers, converted 30 of 41 free throws and got 26 points from Markel Starks in a 71-59 victory at Allstate Arena. ‘‘I thought our first half was absolutely awful,’’ Hoyas coach John Thompson III said. ‘‘[The Demons] made it that way. Their team was playing really hard. In the second half, our guys decided they wanted to play.’’ DePaul (10-13, 2-8 Big East) led by as many as nine in the first half before letting a 30-27 halftime lead slip away because of turnovers and missed shots. ‘‘We went about eight minutes where we didn’t play well, giving them easy baskets, and at the same time we had a drought where we didn’t get a field goal,’’ said Demons coach Oliver Purnell, whose team lost its fifth consecutive game. ‘‘That cost us the game.’’ DePaul played its third consecutive game without leading scorer Cleveland Melvin, who has been suspended indefinitely for undisclosed reasons. ‘‘It was the same old song,’’ said freshman guard Billy Garrett Jr., who scored 12 points off the bench in his return from a two-game absence caused by an illness. ‘‘Turnovers let them back in the game, and we didn’t defend for 40 minutes. Teams like that thrive off turnovers and mistakes.’’