The 28-year-old from Sonora, Mexico, faced trouble during the second inning after giving up a double to Tim Beckham and an RBI single to Jesus Sucre, but Velazquez recovered and struck out Justin Williams, Johnny Field and Daniel Robertson to end the inning.
His efforts even earned him a fist bump from catcher Blake Swihart as he headed back to the bus after the game.
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Velazquez, who had never been to the U.S. until joining Red Sox camp, learned he would be making the start two days ago, after the paperwork for his work visa was processed. He said he's taking everything in from his time with the Red Sox.
"Biggest difference [from the Mexican League], I think, is the discipline that all the players have up here in terms of how they prepare and get ready for games," Velazquez said. "At the end of the day, it's the same baseball -- no matter if you're here or in Mexico. All I have to do is keep doing what I've been doing."
Velazquez has garnered interest from Major League clubs in the past, although he could not remember who they were. In the Mexican League, the teams own the player contracts and clubs have to negotiate directly with each other, instead of the player or player's agent.
Both the Red Sox and the Yankees inquired about Velazquez's services through his club, Piratas de Campeche, but the Red Sox had the advantage because they asked first and their scout Marcus Cuellar had some familiarity with Velazquez.
"He is from the same hometown as me," Velazquez said. "And he has been following me for a while."
Swihart said Velazquez was able to throw his fastball, slider, cutter and change (described as a split-change) for strikes and was in control of his stuff for the full outing.
"He came in with a game plan," Swihart said. "I met with him before the game and he told me exactly what he was trying to do out there and he executed. He's a guy that's mature, he knows what kind pitcher he is and what kind of game he has to throw."
Manage John Farrell said Velazquez looked very comfortable on the mound and with the team, despite being a recent addition to camp.
"[He is] a veteran guy who's been in those situations many times over," Farrell said. "I think in Spring Training, you're always looking to see how guys are going to manage innings as they start to gain momentum against them. Today there was certainly a mixed bag. But I think with Hector in particular, he was very calm and made pitches."