Houston pulled within 3 1/2 games of the wild card with four games left on its schedule, trailing New York and Milwaukee for the top spot.
"This one was a good one for us," manager Cecil Cooper said. "We live to dance a few more days. We just have to keep winning and hope for divine intervention."
Wolf (12-12) allowed eight hits, struck out seven and walked two, improving to 6-2 in 12 starts since being acquired from the Padres on July 22.
"He has been unbelievable," Berkman said. "He's a guy I've always had respect for and wanted us to sign. He has really solidified our pitching staff.
"I think he and LaTroy [Hawkins] are probably the two biggest reasons we are where we're at right now."
"He has been a nice, nice addition for us," he said. "I think only two outings has he not been up to par. His command was a little bit off tonight but he made pitches when he had to."
Cincinnati put runners in scoring position in the second, fourth, fifth, sixth and seventh innings but Wolf managed to work his way out of trouble every time.
"It was definitely a tough one for me," Wolf said. "It seemed like I got two quick outs several times and then it would be crunch time. I was lucky enough to get out of those jams."
Geoff Geary, Hawkins and Doug Brocail pitched the final 2 1/3 innings and allowed only two hits. Hawkins has not yielded an earned run in 22 games spanning 19 innings since coming to the Astros from the Yankees on July 30.
Cincinnati's Ramon Ramirez (1-1) went five innings and allowed two runs and four hits in his fourth major league start.
"Ramirez got a little changeup happy in the first inning and he got one up high to Berkman," manager Dusty Baker said. "He located his pitches much better after the first inning."
Ramirez said his location improved after the first inning.
"The changeup was a high, hard changeup to Berkman," he said. "I was hoping for a groundball or a weak flyball, but I got it up too high.
"I made that one mistake. After that, I was fine."
Berkman drove in Kaz Matsui with a two-out drive to left in the first inning. It was his 29th homer of the season.
Houston RHP Chris Sampson said an MRI revealed a slight tear in his lateral tendon in his injured right elbow. Sampson said he will be available for the rest of the season, then decide whether to have surgery or rehab the elbow. He said he has pitched with some pain for some time. Berkman?s homer was his 44th against the Reds, surpassing Alex Rodriguez?s 43 against the Angels as the most by any player against a single opponent since 2001. Matsui went 2-for-4 and is hitting .417 (10-for-24) since returning from the disabled list Sept. 16. It was the Astros' NL-best 13th shutout. Quintero's hit stopped an 0-for-22 streak. Cincinnati's Joey Votto went 2-for-3 and has two or more hits in six of his last seven games.