In the Eastern Conference semi-final first leg, the Red Bulls led 2-0 at half-time at Houston's BBVA Compass Stadium but the home side fought back after the break, helped by a red card to New York defender Jamison Olave, to snatch a draw.
With the away goals rule not used in the play-offs, Houston will start level with the Red Bulls when the second leg kicks off in New York on Wednesday.
The Red Bulls hit the front in the 22nd minute on Sunday when Thierry Henry's cross to the back post found Tim Cahill and the Australian forward powered his header into the top corner.
The visitors doubled their lead 10 minutes later when Cahill fed Eric Alexander in the right-hand channel and the midfielder burst forward, before cutting inside his marker and beating Houston goalkeeper Tally Hall at his near post.
New York were deserved leaders at the break but six minutes into the second half, the Dynamo hit back when Ricardo Clarke controlled a under-hit clearance on the edge of the box and volleyed through a sea of legs into the back of the net.
The goal gave the home fans some voice and lifted Houston, while Olave's straight red for a two-footed challenge into the back of Cummings saw the Dynamo step up another gear.
After failing to convert a number of chances in the final half hour, the Dynamo finally levelled in the 91st minute when Brad Davis' corner was headed towards the bottom corner by Bob Boswell and although New York's goalkeeper Luis Robles made the initial save, he only managed to parry the ball onto Cummings' foot for the equaliser.
In the Western Conference semi-final first leg on Sunday, Los Angeles Galaxy overcame Real Salt Lake 1-0 thanks to a thunderbolt from Sean Franklin.
The reigning MLS Cup champions dominated Real in the first half with seven corners to zero and 73 passes in their attacking third to Salt Lake's 31.
But despite a number of one-on-one opportunities, LA were unable to break the deadlock before half-time with both Landon Donovan and Robbie Keane failing to convert decent chances.
It took just two minutes of the second half for Franklin to give the Galaxy the lead in front of their home crowd with Keane's cut-back finding the full-back, who unleashed a thumping 30-yard strike past Nick Rimando in the visitors' goal.
While Real took more control of the match after going behind, they failed to produce enough quality goal-scoring opportunities and will face a one-goal deficit when they host the Galaxy in the second leg on Wednesday.
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