The rookie is quickly teaching his manager all about himself.
"You have to give a lot of credit to our scouting department and front office for finding this kid because he gives us a lot of options being a switch-hitter and can play all over the infield," Girardi said.
Solarte, 26, spent time in the minors with Minnesota and Texas but never got called up until this season after hitting .429 this spring.
"I've worked very hard for this, and to be able to help the team, that's even better," Solarte said in Spanish through a translator. "These are the small things that are key."
Solarte singled in a two-run third inning that put New York up 2-1. He doubled in the fifth and scored on a single by Jeter to push it to 3-1.
Houston cut the lead to one in the bottom of that inning before Solarte came through again, this time with a single that drove in Ichiro Suzuki.
Solarte, the third baseman, also had a nifty defensive play when he grabbed a bullet hit right at him by Jose Altuve in the eighth.
Ivan Nova allowed six hits and two runs and walked five in 5 2/3 innings. He was helped by a defense that turned four double plays with him on the mound.
"This could have been a game where he gave up a lot of runs without those double-play balls," Girardi said. "He made big pitches when he had to."
Dexter Fowler continued to shine in his first season with the Astros, getting two singles to become the second player in franchise history -- and first since Ken Caminiti in 1987 -- to begin his Houston career with three straight multihit games.
"We had our chances, especially early on there," Houston manager Bo Porter said. "I think we hit into four double plays in the first five innings. We had baserunners everywhere. It was probably one big hit away from getting some separation early in the game."
Houston starter Brett Oberholtzer also went 5 2/3 innings, allowing five hits and three runs while fanning five.
Suzuki doubled with two outs in the seventh before scoring on the RBI by Solarte. Solarte's hit was a high pop-up that dropped right among three Astros players assembled directly in front of home plate.
Solarte doubled with one out in the fifth and scored on a two-out single by Jeter to make it 3-1. Jeter was thrown out trying to stretch the hit into a double.
Houston got to 3-2 when Jonathan Villar doubled and scored on a single by Fowler in the bottom of the inning. The fourth double play by the Yankees got the first two outs before Chris Carter grounded out to end the inning.
Oberholtzer retired the first seven batters he faced before running into trouble. Suzuki and Solarte hit consecutive singles before a third one by Brett Gardner scored Suzuki to tie it at 1-all.
Jeter walked and Carlos Beltran's sacrifice fly scored Solarte to give New York a 2-1 lead.
Fowler and Robbie Grossman hit back-to-back singles to start the first before Nova plunked Jason Castro to load the bases. Altuve grounded into a forceout that left Castro out at second and scored Fowler to make it 1-0.
Carter walked to load the bases again, but the Yankees turned a double play to limit the damage. The Yankees also used double plays to get out of the third and fourth innings.
Castro also was hit by a pitch in the third inning to become the first Astro since Brad Ausmus on April 7, 2007, to be hit twice in a game. He remained in the game before being replaced by Carlos Corporan in the top of the sixth with a bruise on his right foot. X-rays were negative, and he is day to day.
A replay was initiated by umpires on the field to check the count on an at-bat by Solarte with two outs in the ninth, and it was confirmed it was a 3-1 count. ... Japanese ace Masahiro Tanaka is scheduled to make his major league debut against right-hander Dustin McGowan when the Yankees open a three-game series at Toronto on Friday. ... Houston right-hander Lucas Harrell opposes left-hander Tyler Skaggs when the Astros begin a series with the Los Angeles Angels. ... The Astros observed a moment of silence before the game to remember the victims of Wednesday's shooting at Fort Hood, which left four dead and 16 wounded.