Group C winners and tournament joint favourites Mexico brought a second-string team but started brightly against a nation that progressed to the knock-out stage despite not scoring a goal in any of their three group games.
Jesus Duenas' inviting cross was missed by the entire Honduran defence and Pizarro nipped in at the back post to side foot home from three yards out.
The game took place in a 90-degree Fahrenheit heat in Arizona and neither side was able to dominate a scrappy match.
Mexico had the better of the first half and Honduras improved in the second period, almost grabbing an equaliser direct from a corner kick when keeper Jesus Corona had to look smart to punch out Alex Lopez' inswinger.
One goal was enough, though, to take Mexico to a semi-final tie against Jamaica.
"We knew it would be a hard game and difficult to get behind them as they play deep," Pizarro told TV cameras after the game. "We are getting better each game and the object now is to reach the final."
Jamaica's Shaun Francis put his side ahead after just six minutes with a powerful side-footed shot and Romario Williams doubled their leader five minutes into the second period when he curled the ball into the far corner from just outside the box.
Canada's David Junior Hoilett scored an almost identical goal five minutes later but the Reggae Boyz held on to progress to Sunday's semi-final at the Rose Bowl.
The match will be a repeat of the 2015 final, which Mexico won 3-1 to lift their seventh Gold Cup.
Costa Rica will face hosts the USA in the first semi-final in Dallas, Texas, on Saturday.
The final will be played in Santa Clara on July 26.
(Writing by Andrew Downie; Editing by Amlan Chakraborty)
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