Paul led off the sixth in place of Charlie Morton, and smacked his first double of the season before Jones pinch-hit for Matt Diaz and ripped an RBI single to right field to tie the game at 3.
"That's a momentum shift," Paul said. "They're up, 3-2, right there. We're trying to crawl back, and anything can happen if you get on base. That was my mindset."
Paul finished 3-for-3 and a triple short of the cycle, despite playing only the final four innings.
"If you can just find a way to stay in the game -- know the outs, watch the pitcher, and stay loose -- when you get in there, you just go hard," Paul said.
The Pirates took the lead in the sixth inning on an error by first baseman Brett Wallace, whose errant throw home on an Andrew McCutchen ground ball allowed Jose Tabata to score.
Neil Walker's sacrifice fly in the sixth inning gave the Pirates a 5-3 lead. While McCutchen increased his hit streak to 14 games with a double in the fifth inning, Walker stretched his road-game hitting streak to 11 games with an RBI triple off the glove of a sliding Hunter Pence in the first inning.
Walker also knocked in a run on a rope to center field in the third inning. The Pirates are 10-4 on the road this season when Walker has at least one RBI.
"It's good to see him getting things back together," Hurdle said. "There's some pause in his swing now. There's some separation in his swing. It's more under control."
Catcher Michael McKenry recorded his first Major League hit on a single to left field in the second inning, and added another single in the seventh.
Hurdle said the catcher will get the day off tomorrow afternoon, after being behind the plate for three straight games.
"To get your first hit, it's a special event," Hurdle said. "It really is. It's always nicer when you win, because it's not like you're going to jump around when your team loses."
McKenry scored later in the seventh inning on Paul's two-run shot to left field. Paul's only other home run in his career came on May 15, 2009.
"I haven't hit a home run in over a year, so I had no idea it was going to carry on out," Paul said. "But I did square it up, hit it on the barrel, and it just kept going and going. ... It's a great feeling to know that I put one out."
Morton and Astros starter J.A. Happ both threw more than 100 pitches in five innings of work. Morton threw 109 pitches, allowing three runs on eight hits; while Happ threw 108 pitches, allowing two runs on six hits and four walks.
"Both those starters just threw so many pitches," Hurdle said. "I've got to give Charlie some credit. He battled through. He didn't back away. He didn't want to come out, but the pitch count was what it was."
The start didn't go as smoothly for Morton as his last outing against Houston, when he allowed one run in 7 2/3 innings on May 6 in a 6-1 Pirates victory.
"I thought the guys did a real good job of making him get balls up, and having some long at-bats," Mills said. "We did a good job of getting his pitch count up."
Morton was able to work out of trouble on multiple occasions. The Astros left the bases loaded in the first and third innings.
"Those innings are frustrating, almost as frustrating as giving up runs, because it's a grind," Morton said. "It's seemed like it's been like that for the past five or six starts ... just grinding."
The teams combined to leave 27 runners on base after registering a combined 26 hits. The Pirates were responsible for 13 of those runners, and left at least one runner on base in every inning.
Daniel McCutchen threw three innings in relief, allowing three hits and no runs while striking out one. Chris Resop pitched 1/3 of an inning, allowing a hit and a walk in the ninth before handing the ball to Joel Hanrahan, who notched his 19th save in as many opportunities.
The Pirates are now one game over .500 this late in the season for the first time since having a 59-58 record on Aug. 15, 1999.