After a lacklustre first 45 minutes, the game came to life and the visitors took the lead on 69 minutes when Dillion Powers headed home.
The Rapids went in search of another, but the hosts struck a leveller on 80 minutes when Espindola fired past Zac MacMath.
Both sides came into the game searching for a crucial three points which would see them climb up their respective conference standings, but it was the hosts who had the better start.
Hosts Have The Brighter First Half
Patrick Nyarko was causing serious problems down the flank for the home side, but despite the pressure, MacMath wasn’t tested as much as the Black-and-Red will have hoped.
The visitors almost took the lead on the hour mark when Dominique Badji controlled the ball for Kevin Doyle, who flicked on at goal, but the ball cannoned off the post.
Despite being on the back foot in the opening 45 minutes, the Rapids then came out in the second-half with a point to prove. However, they had to survive a scare on 67 minutes.
The ball came across to an unmarked Steve Birnbaum, who struck a fierce volley just over the bar at the back post.
Rapids Take The Lead Through Powers
United were made to rue that missed chance as moments later their opponents went up to the other end and took the lead in the game from a corner.
Marco Pappa whipped a brilliant ball into the box and Powers got ahead of his marker to nod home past a helpless Travis Worra.
Sam Cronin probably should have ensured all three points travelled back with the visitors, but after substitute Luis Solignac brought the ball down for the midfielder, Cronin could only strike wide of the post.
Hosts Level Late On Through Espindola
D.C. United struck level 10 minutes from the end, and the visitors were also made to rue the missed chance just five minutes before.
MacMath’s attempt to catch Taylor Kemp’s cross fell to the feet of Nyarko, but after Marc Burch blocked his shot on the line, Espindola followed up and made no mistake with the finish.
For the closing stages of the game, the pendulum swung the home side's way, but neither side managed to threaten to go and find a winner in the game.
After their second draw in a row, D.C. United remain at home as they welcome FC Dallas, who have won two of their three games so far this season, to RFK Stadium on Saturday.
Meanwhile, the Rapids are now 1-1-1 and don’t play now until Sunday 3 April, they welcome Toronto FC to Dick’s Sporting Goods Park in two weeks.