Facing Jim Corsi (0-5), the Astros' fourth pitcher, Brett Butler led off the 13th by hitting a single up the middle. Butler was sacrificed to second by Lenny Harris before Kal Daniels was walked intentionally to set up a force for Strawberry.
Strawberry was in an 0-and-2 hole before hitting Corsi's 1-and-2 pitch over the wall in right-center field. It was the Dodgers' seventh hit of the game and allowed them to maintain a 1 1/2-game lead over the Atlanta Braves.
The homer also ended another evening of futility for the middle of the Dodger lineup. Daniels, Strawberry and Eddie Murray had only a single between them through the first 12 innings.
"It's more gratifying to get a win tonight because of all the recent one-run losses," said Strawberry, who has 17 home runs this season. "In that situation, I'm not really looking for a home run, I'm looking to drive the ball. It's a really good feeling to win the ballgame, but it ain't the personal things you do in baseball, it's how the team does."
Kevin Gross, the last of five Dodger pitchers, got the victory to improve to 7-9.
Before a Dodger Stadium crowd of 37,029, the Dodgers failed to capitalize on several early scoring opportunities before tying the score in the eighth inning. The Astros wasted an opportunity to win in the 11th, when their leadoff man singled but was left on base.
The Dodgers' inability to beat the sixth-place Astros had been instrumental in shrinking their lead over the Braves. The Astros had won the last five meetings with the Dodgers and held a 7-4 season advantage going into Friday's game.
The Dodgers looked sharper Friday, making a handful of fine defensive plays and getting strong pitching, but they continued to sputter on offense.
With the Dodgers' recent poor play and lack of offense clouding the pennant picture, this much was clear Friday: Dodger fans are becoming increasingly impatient.
Despite a fine running catch in right field and a score-tying fly ball in the eighth, Strawberry was booed when he struck out on three pitches in the first inning, bounced into a double play in the fourth and popped to left in the sixth.
The Dodgers' vaunted starting pitching has gone into the seventh inning 67 times this season, but the news was not good Thursday, when Ramon Martinez went five innings. And things might have gotten worse Friday, when Orel Hershiser left after one inning, complaining of weakness because of flu and an inability to get his surgically repaired shoulder loose after retiring the side in order.
The Dodgers' hitting woes also continued. After getting five singles Thursday, they had only an infield single through three innings against rookie Darryl Kile. In the fourth they failed to score despite a leadoff walk and two singles, with Strawberry's double-play ball squelching the potential rally.
Another scoring opportunity failed in the fifth when Harris lined into a double play with two men on.
Kile gave up only five hits before leaving in the eighth.
The Astros took a 1-0 lead against Hershiser's replacement, Jim Gott. Gott threw four innings, his longest stint of the season, and was touched for rookie outfielder Mike Simms' first home run of the season in the fourth.
Strawberry got back in the fans' good graces by running down Casey Candaele's long fly ball at the right-field wall leading off the seventh inning, gloving the ball before bouncing off the bullpen fence in a play reminiscent of the one on which he suffered a separated shoulder in May.
Kile, 22, finally tired in the eighth, giving way to Al Osuna with Mike Scioscia on second, Harris on first and one out. Daniels fought back from a two-strike count to walk and load the bases, and Strawberry delivered a sacrifice fly to tie the score.
The runs batted in marked a measure of revenge for Strawberry, who had words with Osuna in Houston. In two previous confrontations, Osuna had retired Strawberry, and announced he would try to strike him out every time.
"He hasn't been around long enough to talk trash," Strawberry said then. "What goes around comes around."
Strawberry came around in the 13th.