His father constantly reminded him "never to surrender, never give up," and those words have been ingrained into his personality.
Velez has talent, works hard and doesn't hesitate to ask questions.
"Even if I think they're stupid questions, I ask. I never thought I would be playing with these guys and I'm learning everything from them," Velez said, referring to Dave Roberts and Omar Vizquel in particular. "They've played the game for 20 years. They know everything about baseball."
Velez, an outfielder for the most part in the Minors, also credited coach Ron Wotus with the development of his infield skills.
"The kid is a battler," Giants manager Bruce Bochy said. "He's out here every day working hard. He competes well. He's still in a learning stage, but he has good tools."
Setting the stage for Velez's heroics, Chris Young tripled home a pair of Arizona runs with two outs in the top of the ninth against closer Brian Wilson, who recorded his second consecutive blown save and his fifth overall. Wilson walked Chris Snyder and Tony Clark ahead of Young's triple. Miguel Montero and Jeff Salazar scored as pinch-runners.
"It looked like [Wilson] was just missing," Bochy said. "He'll be fine. This is all part of being a closer. That first pitch [to Young] got too much of the plate."
Velez, who delivered a walk-off single in Tuesday night's win, doubled off the right-field wall with the bases loaded in the third inning when Arizona outfielder Adam Dunn either lost the ball in transition or tried to fool the baserunners into thinking he would actually catch it.
Velez earned some extra playing time the rest of the way.
"He can play the outfield, second base, he has speed and he's a switch-hitter," Bochy said. "There's a lot to like about him."
There was also a lot to like about Brad Hennessey, who contributed a quality start and was on track to earn the victory before Wilson's struggles.
Alex Hinshaw (2-1) got the final out of the ninth and earned the victory.
Hennessey made one mistake: Stephen Drew's solo home run in the third. He gave up four hits in six innings with three walks and three strikeouts in his first big league start since Sept. 16, 2006.
"It's been awhile, and this was a great opportunity," Hennessey said. "I'm trying to maximize that opportunity. My goal has always been to start, and now I can try and show what I can do."
Bochy said Hennessey earned another start with the effort, although Hennessey said he hasn't heard anything official.
"It's been 12 days since my last start [in Triple-A Fresno], and I can't be displeased," Hennessey said. "I left the game with a lead. I felt like I did what they wanted me to do. Now I want to go out and improve on that."
Hennessey has not won as a starter in San Francisco since July 9, 2005, but he likely earned an encore performance when the Giants travel to Arizona next week.
"My last five or six starts in Fresno, things started clicking for me," he said. "I built my stamina and got into a routine. I feel starting is better for me because I do well with the rhythm."