Houston has been perfect since Rosenfels replaced injured quarterback Matt Schaub, who may miss the rest of the season with shoulder problems. The Texans improved to 7-7 and kept their playoff hopes alive.
They need victories in their last two games to have the first winning record in franchise history.
Denver fell to 6-8, having lost three of its last four.
Rosenfels scored on a five-yard run on the Texans' first possession and threw a four-yard touchdown pass to Andre Johnson early in the fourth period for a 24-13 lead. He completed 16 of 27 passes for 200 yards with an interception.
Notable deaths of 2014 [PHOTOS]