Dunfield headed a shot from 8 yards off the glove of Houston keeper Tally Hall, off the bottom of the crossbar and into the net.
Toronto (5-15-6, 21 points) has two ties in its past four games.
Houston (11-6-9, 42 points) got its second straight draw and is unbeaten in 10 of its past 11 games.
Will Bruin put Houston ahead 1-0 in the 21st minute, taking a pass from Oscar Boniek Garcia, cutting through two Toronto defenders and chipping a shot from 12 yards in the middle over Toronto FC goalkeeper Freddy Hall and into the net.
Je-Vaughn Watson had a shot from the middle of the box in second-half stoppage time saved by Freddy Hall to maintain the tie.
Off a corner kick, Adam Moffatt had his shot go just over the crossbar in the 81st minute.
Bobby Boswell missed a chance to put Houston ahead 2-0 in the 28th minute, just missing wide of the far post on a kick from the left box. Macoumba Kandji had a header saved by Freddy Hall in the 68th minute from the penalty area.
Luis Silva had a shot from the upper box saved by Tally Hall in the fourth minute. Silva had another shot saved by Tally Hall in the 55th minute from 10 yards.