In the sixth, Webb took a hard liner to his left ribcage off the bat of Kevin Kouzmanoff. Webb received a nasty bruise, which he showed off to his teammates during the postgame handshake line.
"That was the worst one for sure [this year]," Webb said of the blow. "They thought I got a glove on it, which I didn't. But I wish I did."
Manager Bob Melvin said after the game that Webb's ribs were not damaged, and Webb said he didn't anticipate any problems going forward.
"It's going to be a couple days of soreness, but it'll be all right after that," Webb said.
San Diego's Chad Reineke (1-1) -- making his second career start -- kept things tight until Jackson's double in the fifth gave the Diamondbacks their cushion.
"That's a big hit right there," Melvin said. "... It really kind of lightened the mood a little bit and gave [Webb] some room to work."
Jackson entered the series with only three hits in his past 25 at-bats, but he went 5-for-12 during the set with six RBIs.
Adam Dunn opened the scoring in the second inning, working a leadoff walk, taking third on Mark Reynolds' double and scoring on Tony Clark's sac fly. Dunn walked three times Thursday, and he has reached safely in 22 of his 41 plate appearances as a Diamondback.
"He's on base every time," Jackson said of Dunn. "There's something to be said for a confidence booster. ... We added a monster."
Young and Augie Ojeda singled in the fifth and scored on Jackson's double. Ojeda punctuated the breakthrough by making a diving stop of Brian Giles' grounder in short right field and tossing to first for the initial out in the sixth.
Jackson doubled again leading off the eighth and, after another Dunn walk, scored on Chris Snyder's single to put Arizona up, 4-0.
D-backs reliever Tony Pena struck out two while retiring the side in order in the eighth. Pena allowed nine hits and seven runs in his first four outings this month, but he hasn't yielded a hit in his past five appearances.
"Boy, it looks like Tony's got his mojo back," Melvin said. "We have very few guys who can throw the ball close to 100 miles per hour with a very tight slider."
Closer Brandon Lyon continued to struggle in non-save situations, losing the shutout in the ninth as Chase Headley singled, took second on defensive indifference and scored on Edgar Gonzalez's single.
Reineke (1-1) yielded five hits, three walks and three runs in six innings, and he came up empty in two at-bats against Webb. Reineke, who was 1-for-2 with an RBI in his first start, grounded out in the third and struck out trying to bunt in the fifth.
"I don't think I've ever bunted a ball that moves like that," Reineke said. "Every one of those pitches he threw me looked like a strike. ... It looks good coming at you, but right when it gets to you, it just drops. He made me look pretty foolish out there."