The injuries were piling up but had seemed short-term. And Saturday, the Rockets were overcoming them.

Then they got worse, and more long-term than the run of health problems that has required a revolving door on the training room since opening night.

Rockets guard Pat Beverley left Saturday’s game with a fractured right hand. He said he was told he had fractured the fourth metacarpal in the hand and would be out four to six weeks.

More extensive tests and a visit to a specialist are scheduled for Sunday, but the remarkable run of injury problems had gone beyond nuisances.

Yet, while the Rockets lost player after player, the one who has competed in every game this season would not let the Rockets lose a game, too. Dwight Howard dominated from start to finish, scoring a season-high 35 points to lead the shorthanded Rockets past the Pistons 114-97.

Beverley and Greg Smith went out during the game. James Harden was ruled out before the game because of his sore ankle. Jeremy Lin was at least a game away from returning from his sore back. Omer Asik was in Houston with his sore knee.

For all the injuries that have marked the season — with players combining to miss as many games as all of last season — Beverley’s will be the most long-term.