It was Asche's third hit of the game.
Chapman finished matters by striking out pinch-hitter Cesar Hernandez for his second save.
Once again, Phillies righthander Kyle Kendrick had another strong showing and got nothing but a big "L" to show for it.
In the first inning, Kendrick opened by allowing singles to Hamilton and Skip Schumaker. On Schumaker's hit, leftfielder Domonic Brown hesitated on a catchable ball that fell in front of him.
"I just didn't think I could get to it," Brown said. "I didn't want to force it and make a diving play there and see it get past me."
Kendrick then got the next two batters and he could see his way out of the inning.
Reds catcher Devin Mesoraco didn't oblige, smoking an 88 m.p.h. 2-1 cutter for a three-run homer to left.
"I didn't want to go 3-1, I wanted to throw a strike there and it was up a little bit," Kendrick said. "He ended up getting it out of there."
Kendrick threw 23 pitches in the first inning, but settled down afterward. After Mesoraco's homer, Kendrick retired the next 15 batters until Brandon Phillips got an infield single with two outs in the sixth inning.
Kendrick allowed three runs on four hits in seven innings, walking one and striking out five. In eight starts, he has allowed three earned runs or fewer six times. His ERA is 3.96.
"First innings have been tough for me, and it is something I need to work on," Kendrick said. "I have to try to be more aggressive in the first or something but after the first I tried to keep us in there."
Meanwhile Reds starter Alfredo Simon, kept pitching out of jams the first five innings. The righthander got Marlon Byrd on an inning-ending strikeout with two on in the first and Ryan Howard to end the third, also with two men on base.
After Asche led off the fifth with a double, Simon got two strikeouts sandwiched around a groundout. Through the first five innings, the Phillies were 0-7 with runners in scoring position.
Simon exited after allowing a two-out single to Chase Utley in the eighth inning, but lefthander Manny Parra ended the inning by striking out Ryan Howard.
Simon pitched 72/3 innings, allowing five hits, striking out eight, and walking one.
Ben Revere was out of the lineup with a stomach virus, and Jimmy Rollins held the lead-off spot for the first time this season. Sandberg was looking to do anything to shake the lineup.
Carlos Ruiz batted second. In four previous games in the two-hole, Ruiz was hitting .571 (8 for 14) with a 1.557 OPS. Against the Reds (19-21), he reached base twice, getting hit by a pitch and drilling a third inning single.