Nolan Arenado also homered to extend his hitting streak to 25 games. It is the longest in the majors this season.
Tulowitzki, who was named the NL Player of the Month for April before the game, had his first multi-homer game of the season and the ninth of his career. He hit a two-run shot off Texas starter Martin Perez in the fifth and hit another two-run homer off reliever Shawn Tolleson to give Colorado a 7-1 lead in the seventh.
It was more than enough for Lyles (4-0), who came within three outs of the second complete game of his career.