"We've had that problem more than a few times this year," said Hamilton forward Patrick Holland, who scored his team's only goal late in the first period.
"It's too bad, because we start playing really well when we get down a couple of goals. If we could come out with that sort of attitude to begin a game, I'm sure a lot of them would have ended differently."
Jacob Markstrom made 30 saves in goal for San Antonio — 16 of those in the third — as Colby Robak, Drew Shore, Dylan Olsen and Vincent Trocheck scored for the Rampage (22-21-8).
Robert Mayer stopped 26 shots in the losing effort for the Bulldogs (22-23-5), who have lost seven of their last nine games.
San Antonio opened on a power play as Robak took a pass from Greg Rallo and released a high, heavy shot over Mayer's shoulder at 9:16 of the first period.
The Bulldogs used the forecheck to score the tying goal at 18:48 as Martin St. Pierre flicked a centring pass in front that clipped the skate of Holland as he skated through the slot and slid past Markstrom.
Hamilton head coach Sylvain Lefebvre was disappointed they were unable to build on the goal.
"When you get a big goal to end a period and tie things up and then start the next period flat, it's not acceptable," he said.
It took less than a minute for the Rampage to break the deadlock in the second period on an odd-man rush with Rallo shooting and Shore swatting in the rebound just 23 seconds into the period.
Less than two minutes later, San Antonio increased its lead when Olsen's wrist shot caught beat Mayer through the five hole at 2:01.
Lefebvre called a time out to settle his group.
"(Lefebvre) told us not to blame (Mayer)," said Holland of the message at the break.
"That third goal wasn't the prettiest thing but everyone makes mistakes in this game. When it happens to a goalie, you feel bad for him, but the important thing is to stay with him. He made so many huge saves for us, so when something like that happens, we have to look at it as our job to bring one back for him."
Hamilton had a chance to cut the deficit 10 minutes into the period when Christian Thomas stole the puck in the low slot and snapped a wrist shot over Markstrom's crossbar.
Trocheck put the game away when he scored into the empty net at 18:24 of the third. Hamilton's power play was shut out for the second straight game, as the Bulldogs went 0-4 with the man advantage. San Antonio was 1-1.