Beverley, who injured his ribs in Wednesday's season opener, will miss 10 to 14 days as he recovers.
Lin started Friday night's 113-105 victory over the visiting Dallas Mavericks, scoring 14 points.
"I'm taking precautions to make sure I'm 100 percent all right," Beverley said Friday, according to the Houston Chronicle. "If this was the playoffs, I would play tonight for sure. I'm going to go crazy over here sitting like I'm a coach with a suit on, but I can root my team on and look at the game differently, maybe see some things that I don't see while I'm out there and try to add to my game when I get back."
Beverley injured his ribs in the second quarter of a 96-83 win over the Charlotte Bobcats and didn't return. Lin was also hurt and required stitches to his chin but returned to the game.
Beverley finished with five points. Lin had 16.
"I'll still be the same player," Lin said of his return to the starting lineup, according to the Chronicle. "Obviously, we need Pat, and we need Pat to play at a high level for us to be where we want to be. He has to get healthy. Other guys have minor injuries, too. Everybody needs to get healthy."
Information from The Associated Press was used in this report.