Leake, who signed an $80 million, five-year contract in December, has 24 strikeouts and two walks in 20 spring innings. He threw 33 of 39 pitches for strikes.
"I don't worry about that," Pineda said. "I feel great."
Jeremy Hazelbaker added a three-run homer in the fifth. Tommy Pham had a two-run shot in the seventh.
Pineda gave up six runs and seven hits over five innings. He had given up just one run in nine earlier spring innings.
"I thought he threw the ball better than his numbers indicated," Yankees manager Joe Girardi said. "I'm not so sure how many of those are home runs if the wind is not blowing (out). But I thought he threw pretty good."
Rodriguez was hitless in three at-bats and is hitting .273 (12 for 44) overall. After homering on his first at-bat of spring training, A-Rod has not gone deep in 43 since. The homer is his only extra-base hit.
Yankees: Girardi said Masahiro Tanaka will start on opening day and be followed in the rotation by Pineda, Nathan Eovaldi and Luis Severino. The manager said meetings are continuing to decide if CC Sabathia or Ivan Nova will be the fifth starter.
Yankees: Closer Andrew Miller plans to pitch through a chip fracture on his non-throwing wrist. He was hit by a liner in Wednesday's game against Atlanta. He will see a hand specialist Saturday ... Long man and spot starter Bryan Mitchell could need surgery after breaking a bone on his left big toe covering first base Wednesday. He could miss several months if surgery is required.
MOLINA IN MOTION
Cardinals C Yadier Molina had an infield single in the second and then stole second base uncontested. It was his first stolen base this spring. Molina has 44 stolen bases in 1,464 regular-season games.
Girardi said Austin Romine will be New York's backup catcher. Luis Cessa and Johnny Barbato made the team as relievers, and right-hander Anthony Swarzak and outfielder Cesar Puello were reassigned to minor league camp.
Cardinals: St. Louis will work out Saturday in Pittsburgh, one day before Adam Wainwright faces the Pirates on opening day.
Yankees: Eovaldi will go against Miami's Jose Fernandez on Friday night in the opener of a two-game, spring training-ending series at Marlins Park.