Williams kept on making his case Sunday, winning a third straight start for the first time since April 2004 as the Angels beat Houston, 2-1, to send the Astros to their 98th loss.
Houston, a big league-worst 51-98, is on the verge of becoming the first major league team to reach triple figures in losses in three consecutive seasons since Kansas City from 2004-06. The Astros were 56-106 in 2011 and dropped to 55-107 last year, their final year in the National League.
Williams (8-10) entered following wins over Tampa Bay and Toronto, and he gave up one run and five hits in seven innings.
"This team is a real good team," said Williams, who began the season in the bullpen. "I would love to come back and be part of this team and hopefully make that run for next year."
A veteran of 10 seasons, Williams knows he has to produce.
"I just have to keep on working," Williams said. "I think I have two more starts, and I just have to keep building on it.
"I can't control what happens after; all I can control is what I'm doing on the mound right now. That's what I'm trying to do, and let everything else fall into place."
Angels Manager Mike Scioscia said Williams has pitched solidly since moving into the rotation in May.
"He's given us chances to win," Scioscia said.
Williams benefited from solid defense and a two-inning relief appearance by Ernesto Frieri, who earned his 34th save in 38 chances.
"It was a good defensive game for us," Scioscia said.
Josh Hamilton had a run-scoring triple in the first against Paul Clemens (4-5), a drive off the glove of center fielder Brandon Barnes as he went up Tal's Hill. Mike Trout had reached base with his AL-leading 100th walk.
"There aren't many ballparks that would hold that ball," Scioscia said. "I think that in any other ballpark we're playing that's a two-run home run."
Andrew Romine hit a sacrifice fly in the fifth after singles by Erick Aybar and Hank Conger.
Frieri entered with two on in the eighth and got six outs, including four via strikeout.
"It's certainly not our preference to have him go six outs, especially when he's got to throw 25 to 30 pitches, but he felt good today and over the course of the last 10 days he hasn't been out there that much," Scioscia said. "He felt fresh."
Frieri said he appreciated the trust.
"This time of the season, I'm 100% ready to go," Frieri said. "Whenever they call for you down in the bullpen, you have to be ready, mentally and physically."
The Angels have won five of six overall and 14 of their last 17 road games.
Class-A Inland Empire beat San Jose, 3-1, Saturday night to sweep the best-of-five California League championship series, the first title for an Angels California League affiliate since 1996. Andy Workman, who drove in two of his six runs of the series in the decisive game, was named series most valuable player.
The Angels' double-A Arkansas team reached the Texas League championship series and extended San Antonio to five games but lost, 5-0, in Sunday's decisive game.
The Angels' triple-A Salt Lake affiliate also reached the Pacific Coast League championship series but lost to Omaha, 10-5, Saturday night to lose the best-of-five series, 3-1. Omaha posted one-run victories in the first two games, and Salt Lake won Game 3 by a 9-0 score.
Times staff writer Mike DiGiovanna contributed to this report.