To that end, Boston's J.D. Drew worked a bases-loaded walk to score another run before catcher Jarrod Saltalamacchia capped the inning with a two-run single to center.
That was more than enough support for Beckett. A Houston native, the Red Sox right-hander cruised against his hometown team, allowing just one hit while striking out three in five innings.
"You talk all Spring Training about how numbers don't mean anything, and they don't," Red Sox manager Terry Francona said. "And when he comes out tonight, and his fastball has that kind of life, that's fun to watch."
In addition to his fastball, Beckett's changeup on Wednesday was as good as it has been since he joined the Red Sox.
"It was good for me tonight," Beckett said. "I don't think I threw too many curveballs for strikes. Maybe two. They really weren't swinging at it, so I had to have something to get it off the end of the bat. The changeup was big for me. I feel healthy."
Boston struck again against Figueroa in the fourth, when Jacoby Ellsbury drove in Saltalamacchia with a double and Crawford singled in two more.
Ellsbury and Saltalamacchia paced the Red Sox's offense with three hits each.
Figueroa, slated fifth in Houston's starting rotation, lasted just three-plus innings, allowing eight runs on nine hits with four walks. He threw 80 pitches with only 46 for strikes.
Brett Wallace, Chris Johnson, Carlos Lee and Matt Downs each singled for the Astros.
Boston finished its exhibition slate 14-19, while Houston dropped to 11-24.
Up next for Red Sox: Boston opens its regular season with a three-game series at defending American League champion Texas starting at 4:05 p.m. ET on Friday, as Lester goes up against left-hander C.J. Wilson. It's the third consecutive year in which the Red Sox have opened against the defending league champion. Lester will become the 12th left-hander to start for Boston on Opening Day, and the first since David Wells did it in 2005.
Up next for Astros: Houston begins its year with a three-game set against the vaunted Phillies rotation, which features Roy Halladay, Cliff Lee and former Astros pitcher Roy Oswalt. In Friday's opener at 12:05 p.m. CT, the Astros will counter with Myers. The former Phillies pitcher was a pleasant surprise in 2010, going 14-8 with a 3.14 ERA, tops in Houston's rotation. That earned him a two-year contract extension with a third-year option. Myers is the first Astros pitcher other than Oswalt to start Opening Day since 2002.