The tie brought the Impact (13-9-7) its first point in three matches (0-2-1), while the single point for Chicago left the Fire (11-12-7) two points out of the last playoff berth in the Eastern Conference with four matches remaining.
Tissot tied it for Montreal in the 87th minute. Left alone in the left side of the penalty area, he took a loose ball and deftly headed it past sprawling goalkeeper Sean Johnson.
Fire forward Mike Magee scored twice in a 16-minute span, putting Chicago ahead 2-1 in the 73rd. He also sent a penalty kick off the crossbar.
Di Vaio's league-leading 19th goal had given the Impact a 1-0 lead in the 25th.