The Dynamo were down 2-0 in the first half but then rallied for a pair of goals in the Eastern Conference semifinal matchup.
Ricardo Clark took advantage of a botched clearing attempt by Red Bulls defender David Carney in the 51st minute to cut Houston's deficit.
New York was reduced to 10 men in the 65th minute when Jamison Olave was given a straight red card for a tackle on Cummings.
Then in extra time, Cummings put in a header from Bobby Boswell for his first goal of the season, drawing the Dynamo even as the series moves to New York for Wednesday's second leg.
Tim Cahill and Eric Alexander each scored for the Red Bulls.
Notable deaths of 2014 [PHOTOS]