"No, I'm not surprised because it's been an eight-year process for me to get where I'm at,'' Leake said. "I'm not surprised for myself, but I'm sure it is a surprise for others.''
Molina, who went 1-for-5, extended his hitting streak to 13 games with a solo blast off reliever Sergio Romo in the seventh inning and the Cardinals (23-20) won for the 10th time in their past 11 games on the road. It was the fourth homer for Molina this season.
"Good at-bats and just fun to watch him to do his thing on a consistent basis," St. Louis manager Mike Matheny said. "Looks strong, feels good and he's taking real strong at-bats. He's got just a great idea of how to play the game."
Leake (5-2) gave up a run with five strikeouts and no walks, lowering his ERA to 1.91. He threw 98 pitches, 60 for strikes. Reliever Tyler Lyons pitched a 1-2-3 ninth.
The Cardinals took advantage of an erratic performance by Dodgers starter Rich Hill and staked Leake to an advantage that he refused to relinquish.
"Any time you can get a lead it's always nice to be able to not have that pressure," Leake said. "But sometimes having low-scoring games help you stay (focused) in the game. It was a good all-around game, great defense. (Shortstop Aledmys) Diaz made quite a few great plays. The infield was working hard today."
Kolten Wong, who was 1-for-3, drove in two runs for the Cardinals.
Hill (1-2) had an awful outing, walking a career-high seven and yielding a season-worst five runs on four hits in four-plus innings. He threw 82 pitches (40 strikes). Hill struck out four.
The Dodgers issued a season-high nine walks.
"Bad outing. It was terrible," Hill said. "I take full responsibility for that, just gave them the game. That's unacceptable. It's really a tough thing to swallow."
Hill said his mechanics were off and he had trouble throwing an effective breaking ball. Although he has had blister problems on his middle pitching finger in the past that landed him on the disabled list, there were no such issues.
Hill also was perturbed with the strike zone of umpire plate umpire Rob Blake.
"I just felt there were a few pitches that were strikes that fell in with the curveball. To me, they looked like strikes," Hill said. "It's just one of those things. You have to adjust to it."
Roberts almost pulled the hook on Hill in the third inning but decided against it.
"I was going to go get him but I think for me, I know he's an emotional pitcher, but you have to compose yourself in some capacity and still try to execute pitches," Roberts said. "I felt right there that he did and made some good pitches on some good hitters and got out of that inning."
Hill retired the side in the first, but his performance took a dive from there. Hill issued walks to Jedd Gyorko, Diaz and Randal Grichuk to load the bases with one out in the second. Wong lined a two-run single to left center, scoring Gyorko and Diaz, for a 2-0 St. Louis lead.
Hill walked Leake to load the bases again in the inning but retired Dexter Fowler on a fly out to second and fanned Stephen Piscotty to get out of the jam.
In the fifth, the Cardinals added three more runs. After Piscotty walked and Carpenter reached on a bunt, Gyorko singled to left. The ball rolled past Bellinger, allowing Piscotty and Carpenter to come home for a 4-0 advantage.
Molina's sacrifice fly plated Gyorko for a 5-0 edge.
NOTES: Dodgers CF Joc Pederson, who sustained a neck strain after a collision with RF Yasiel Puig on Tuesday, was held out of the lineup. Although Pederson passed concussion tests after Tuesday's game, manager Dave Roberts said Wednesday the medical staff was still monitoring Pederson. ... 1B Matt Carpenter became the fastest Cardinal to reach 400 walks (759 games) by reaching in the third inning off LHP Rich Hill. That topped former Cardinal Albert Pujols' mark in 789 contests. ... Dodgers OF Andrew Toles, who underwent surgery to repair his right ACL on Tuesday, celebrated his 25th birthday. ... Cardinals RHP Michael Wacha (2-1, 2.74 ERA) will oppose Dodgers RHP Kenta Maeda (3-2, 5.03) in Thursday's series finale.