Myers (1-0) limited the Cubs to eight hits and one run in seven innings to improve his career record against Chicago to 11-3.
Houston scored three runs off Cubs starter James Russell (1-1) in the first inning, two more in the second and built a 7-0 lead after Sanchez knocked in two runs with a single in the fourth inning.
Russell was making his first career start after 59 relief appearances as a replacement for the injured Andrew Cashner. Russell allowed seven hits and five runs in 1 2-3 innings.
Bench coach Al Pedrique managed the game for Houston with manager Brad Mills serving a one-game suspension for his weekend ejection against the Marlins.
Jeff Fulchino pitched a scoreless eighth for Houston before Aneury Rodriguez allowed one run in the ninth. Rodriguez was given a three-game suspension for his ejection that led to the ejection of Mills. But he is allowed to play while appealing his suspension.
Hunter Pence had four RBIs and Michael Bourn scored a career-high four runs to combine with Sanchez for an outstanding punch at the top of Houston's lineup. Humberto Quintero tied a career high with three hits and fell a home run shy of the cycle.
Tyler Colvin had a solo homer to right field that made it 7-1 in the seventh inning. Marlon Byrd went 3 for 3 with a double for the Cubs. He also robbed Bill Hall of a hit with a nifty leaping catch just in front of the bullpen in right field in the fifth inning.
The Astros hit three straight singles to start the first inning capped by Pence's run-scoring one that made it 1-0. Hall singled and Alfonso Soriano was charged with an error when he couldn't handle the catch, allowing two runs to score and push Houston's lead to 3-0. Hall was involved in a rundown between first and second base on the play, but evaded Darwin Barney to reach second and give Barney an error.
Quintero doubled before a single by Myers in the second inning. Bourn grounded into a force out to score Quintero and make it 4-0. The speedy center fielder then stole second and third base before scoring on a single by Pence that made it 5-0.
Sanchez had a two-RBI single in the fourth inning to extend Houston's lead to 7-0.
Pence drove in two runs with a double in Houston's four-run eighth inning to make it 11-1.
Jeff Samardzija, who was the second of five pitchers used by the Cubs, allowed three hits and two runs in three innings.
NOTES: Chicago OF Kosuke Fukudome was out of the lineup for the second straight day on Tuesday after straining his hamstring making a catch on Sunday. He is listed as day to day with the injury and the Cubs are hoping he will be able to play by Friday. ... Chicago signed veteran pitcher Doug Davis to a minor league deal on Tuesday. Davis went 1-4 in eight starts for Milwaukee last season, but missed most of the year with injuries. Cubs general manager Jim Hendry said Davis will be in extended spring training for a couple of weeks and they hope to have him at Triple-A Iowa before the end of the month.