PITTSBURGH -- Gerrit Cole is off to a perfect start in the major leagues. The rookie, however, feels he has been far from perfect.
Cole (2-0) allowed three runs on seven hits and no walks in 5 2/3 innings. The top pick from the 2011 draft won in his big league debut last week.
"I'm really happy to be able to come up here and pitch well enough to help the team win," Cole said. "But I also know I need to do more.
"I've only gone 6 1/3 and 5 2/3 innings in my two starts. I need to get deeper than that. We're getting the point in the season where the bullpen is going to start having aches and pains and I need to eat up more innings to help those guys out. That's why I'm here," he said.
Cole wasn't as sharp as he was in his debut against San Francisco when he took a shutout into the seventh inning. Pirates manager Clint Hurdle was pleased with this outing.
"He had to compete. He had to go out and battle," Hurdle said. "He knows how to pitch. He knew how to get outs when he needed them."
Alvarez snapped a 2-all tie when he connected off Zack Greinke (3-2) for a three-run homer in the fifth. Alvarez leads the Pirates with 15 homers.
"We needed someone to click one with men on base and Pedro clicked one," Hurdle said.
Alvarez's father, also named Pedro, was in the stands for Father's Day. The elder Alvarez moved his family to New York from the Dominican Republic when his son was 1 year old, and dad made a living driving a livery cab.
Alvarez also hit a home run against the Mets in New York on Mother's Day.
"It just makes it extra special," Alvarez said.
Dodgers rookie Yasiel Puig got three hits and raised his batting average to .479 in his first 48 at-bats in the majors.
Greinke (3-2) was touched for five runs and eight hits in five innings. He walked two and struck out three.
Greinke started for the first time since pitching -- and getting hit by a pitch -- in Tuesday's game against Arizona that wound up in a brawl. Eight people were suspended, and Greinke was among four others who were only fined.
Los Angeles lost for the sixth time in eight games.
There were two outs and no one on in the fifth with the score tied at 2 when Jones singled and Neil Walker walked. Alvarez, who was 1 for 14 in his career against Greinke, then hit a drive into the shrubbery in dead center field.
"The main thing was some big situations came up and I made bad pitches in important situations," Greinke said. "That's what happened."
After Jones gave the Pirates a 2-0 lead in the first, the Dodgers tied it. Puig led off the second with a single, stole second and scored on Tim Federowicz's groundout. Andre Ethier hit an RBI single in the fourth.
Los Angeles closed to 5-3 in the sixth as Ethier singled home Adrian Gonzalez, who had doubled.
The Pirates got the run back in the bottom of the inning when Presley hit his second homer into the right-field stands off Matt Guerrier.
The Dodgers fell a season-worst 10 games under .500 at 29-39.
"It's been kind of the same story and that's that we haven't been able to win a series," manager Don Mattingly said. "We were in a position to win this series and had Greinke on the mound and we didn't get it done again."
Puig is likely to stay in the majors even when OFs Matt Kemp and Carl Crawford are activated from the disabled list, Mattingly said before the game. ... Los Angeles 3B Juan Uribe was a late scratch from the starting lineup because of tightness in his back but was available to pinch-hit. . Pittsburgh C Russell Martin was in the original starting lineup then removed because of lower body soreness. ... Pirates LF Starling Marte did not start for the fourth straight day because of a strained left oblique muscle but entered the game in the sixth inning as part of a double switch. ... Pittsburgh opens a four-game series at Cincinnati on Monday night with LHP Francisco Liriano (5-2, 2.36) facing Reds RHP Mike Leake (6-3, 2.76). ... The Dodgers are off Monday, then open a two-game series Tuesday night against the Yankees in New York. It will be Mattingly's first trip in uniform to the Bronx since the Yankees passed him over and hired Joe Girardi as manager following the 2007 season.