Paul was claimed off waivers from the Los Angeles Dodgers on Wednesday and made an immediate impact. He hit a two-run triple to key a four-run rally in the second and added a single in the fourth.
"My mindset going into the game was just have fun," he said. "To come up with a big hit, it feels great."
Paul, who joined the team Thursday, had his first multihit game since July 20, 2010.
"He was on base three times, stole a base, handled his chances in left field, so it was a good first start for him," Pirates manager Clint Hurdle said.
Charlie Morton pitched into the sixth inning for his third win, Garrett Jones had two hits and Andrew McCutchen, Lyle Overbay and Pedro Alvarez also had two hits each for the Pirates, who took two of three at Coors Field. Pittsburgh won its fourth road series of the season, matching its total from the 2010 season.
Colorado ace Ubaldo Jimenez (0-2) struggled again. He threw three wild pitches, tying a club record, and his ERA rose to 7.20 through four starts.
"Before, I was trying to get my velocity back," he said. "Right now I don't have the control."
Jimenez allowed four runs on six hits, struck out six and walked four. He needed 88 pitches to get through four innings in his shortest outing of the season. Last year, Jimenez failed to pitch into the sixth twice in 33 starts and dominated hitters en route to a 15-1 record at the All-Star break.
"Ubaldo lacked consistency today," Rockies manager Jim Tracy said. "He did not command, he had deep counts."
Morton (3-1) battled until the sixth when Seth Smith led off with a single and Chris Iannetta drew a one-out walk. Mike Crotta relieved and walked pinch-hitter Jonathan Herrera to load the bases. Fowler followed with a double to make it 8-4, but Beimel came on to strike out Alfredo Amezaga on three pitches and retire Helton on a deep fly to left.
"I kept him in my back pocket. Nobody knows this ballpark on our staff better than him," Hurdle said. "He pitches with a slow heartbeat, he's not going to get rattled, and when he's good and effective and hitting his spots he's tough to put the barrel on."
Beimel, who was with the Rockies last season, said the familiarity worked both ways.
"They know me pretty well, too," he said. "I don't think it's coincidence the only two guys who struck out were two that weren't here last year. The other guys knew what I was going to throw them and they know my strengths and weaknesses."
The Pirates jumped on Jimenez in the second inning. Ryan Doumit led off with a walk, Alvarez singled to put runners at the corners and Ronny Cedeno's bunt down the first base line gave Pittsburgh a 1-0 lead.
Jimenez retired the next two batters before Paul tripled to right-center and Jones doubled to center to make it 4-0.
"Ubaldo's a great pitcher, but he made a mistake," Paul said. "You've got to make him pay for it."
The Rockies broke through in the third on Helton's two-out single that scored Fowler from second to make it 4-1. Ryan Spilborghs cut the lead to 4-2 with a pinch-hit single to score Smith in the fourth.
The Pirates broke the game open with a four-run fifth against reliever Esmil Rogers. Morton knocked in his second career RBI on a sacrifice fly and Jones had a two-run single to make it 8-2.
Four pitchers held the Colorado record with three wild pitches. Jimenez was the last to do it, on April 25, 2008. ... Pirates OF Jose Tabata (right hamstring) was held out of the lineup.