Dynamo went from being in a position of total control at 2-0 ahead during the first half to having to settle for a draw.
However they could have few complaints, having allowed Rapid to dominate the second 45 minutes from start to finish.
Dynamo led from the 30th minute when Andriy Yarmolenko struck, and a most unlucky own goal four minutes later from Christopher Dibon gave them their two-goal cushion.
Guido Burgstaller began the fightback by netting in the eighth minute of the second half, and just when it seemed their effort would bring no reward Rapid's Trimmel proved their saviour.
Dynamo had lost their group-stage opener to Genk, while Rapid slid to defeat against Thun, so this was a chance to make up ground.
For the visitors, Younes Belhanda and Miguel Veloso lifted early shots over the Rapid crossbar and Danilo Silva cracked a 25-yard drive off target.
With pressure building, the opening goal duly arrived. Benoit Tremoulinas ran down the left, hugging the touchline, and trickled over a low centre that the home defence might have dealt with better. Instead it reached Yarmolenko, lurking near the penalty spot, and his left-footed strike found the bottom left corner.
Dynamo's second came when Belhanda and Stefan Palla jostled for the ball inside the penalty area, with Rapid left-back Palla getting a toe in to seemingly eliminate the goal threat. Yet the ball arrowed straight at the shoulder of Dibon who at close quarters had no time to adjust, and goalkeeper Jan Novota was wrong-footed.
The seeds of a comeback were sown before the break as Rapid began to pour forward, and the crowd had cause to believe when Palla set up Burgstaller in the 53rd minute. A cross from the left found the Austria international striker who converted a right-footed shot from 12 yards.
Terrence Boyd, Louis Schaub and Burgstaller each went close in the subsequent three minutes, the latter when Maksym Koval had to tip the ball wide for a corner.
Still they piled on the pressure, Brian Behrendt clearing the bar from 20 yards before Koval turned away a 30-yard free-kick strike from Thanos Petsos.
Dynamo flickered to life when Novota needed to be sharp to push aside a shot from Dieumerci Mbokani.
But Petsos was at it again from long range soon after, as the match entered stoppage time, sending his 25-yard attempt wide of the left post. And then came the leveller, Palla involved in a goal for the third time in the game as his cross again from the left picked out Trimmel, and from six yards he rose well to head home.