The Timberwolves led by 18 at the half in their bid for a rare road win, but Houston scored 69 points over the final two quarters.
Harden produced 37 points and had seven rebounds along with eight assists. Lin also handed out eight assists to go with his 24 points. Lin's 3-pointer with 5:30 put Houston ahead to stay at 89-86.
The Rockets and Timberwolves teamed to put up 55 3-point shots and made just 17 of them.
Derrick Williams and J.J. Barea both scored 19 points for Minnesota, which has won on the road just seven times this year.