The 10th-ranked Spaniard, who won at San Jose and Barcelona earlier this year, nearly lost for the fourth time in five matches since reaching the round of 16 at the French Open.
"I was just trying to play my best to the end," Verdasco said. "Even match points down I was just trying to put the ball in and make him put the ball in."
US second seed Andy Roddick, a three-time Washington champion, defeated Slovenian qualifier Grega Zemlja 6-4, 6-4, to reach the third round as well.
Roddick won the only two break-point chances of the match to cruise in 84 minutes and book a third-round match against Frenchman Gilles Simon, who ousted Russian qualifier Igor Kunitsyn 6-1, 6-2.
Verdasco will next face US qualifier Ryan Sweeting, who ousted Frenchman Michael Llorda 6-4, 6-2, on Thursday for a spot in the Friday quarter-finals of the 1.4 million-dollar hardcourt event, a US Open tuneup.
Berrer, ranked 47th, roared ahead 5-2 but squandered two match points in the ninth game of the second set with errant backhands and was broken by Verdasco in the ninth and 11th games to set up a third set that went the distance.
"When I broke back, I started to get confidence and started playing much better," Verdasco said. "Those games were the turning point of the match."
At 6-6 in the tie-breaker Verdasco hurt his left big toenail and stayed on the court briefly, then rose and won the match when Berrer sent a forehand long and a backhand into the net.
"I hit it really hard," Verdasco said of his toe. "It was just a really big pain for about a minute."
US fifth seed John Isner was set for a later match with Thiemo de Bakker, the Dutchman who eliminated him in the second round at Wimbledon after his epic 11-hour opening victory over France's Nicolas Mahut.
American Mardy Fish, whose ranking has soared as his weight falls, stretched his career-best win streak to 11 matches by beating Serbian Viktor Troicki 6-4, 6-3. He won titles last month at Newport and Atlanta and has jumped from 79th to 35th in the rankings since dropping 33 pounds to a trim 170.
"It can all be traced back to it," Fish said. "I'm now able to train and do things I couldn't in the past. I'm able to get to shots I used to not get to. I feel like a completely different player, a completely different person."
Next for Fish will be Croatian fourth seed Marin Cilic, who eliminated Uzbek Denis Istomin 6-4, 6-2.
Serbian Janko Tipsarevic defeated France's Arnaud Clement 6-4, 6-0, to book a second-round match against US sixth seed Sam Querrey, who beat Tipsarevic in a Los Angeles semi-final last week on the way to his fourth title of the year.
Taiwan's Lu Yen-Hsun, who beat Roddick to reach the last eight at Wimbledon, lost 7-5, 6-1 to Colombia's Alejandro Falla in a first-round match.