Despite the return of Lionel Messi to the starting line-up, after he missed the 0-0 draw at Orlando on Wednesday, Miami struggled to create chances against a very well organised D.C. defense.
Ecuador international striker Campana, who has lost his starting place to Luis Suarez this season, was brought on in the third minute of stoppage time and scored with his first touch.
Campana made a darting, diagonal run across the D.C. back line and was picked out by Sergio Busquets, bringing down the lofted pass and then blasting an unstoppable shot past Alex Bono.
It was a cruel end to the game for Troy Lesesne's team, who look vastly improved on the performances they produced under Wayne Rooney last term.
With the win, league leaders Miami clinched their ninth victory of the season - matching their total for last season after just 15 games.
The start of the game was delayed by 25 minutes due to lightning and 15 minutes after the game began there was a torrential downpour.
Miami enjoyed the vast majority of possession in the opening 45 minutes, with the visitors appearing happy to concede the ball while keeping their shape and aiming to counter.
That approach almost paid off, after the break, but Jared Stroud missed a glorious opportunity, poking hesitantly wide from close range.
Messi had been restricted to two free-kick efforts, which both struck the wall, and the Argentine - who missed the midweek game with a knee injury - was well below his best.
D.C. grew into the game and Matti Peltola flashed a shot just wide in the 69th minute.
Two minutes later, Messi found space in the inside-left channel, bringing a high ball down with his chest but he blasted his shot just over the bar.
United had a chance to win the game in the final moments of regulation after a smart move but Cristian Dajome's meek shot was parried away by Drake Callender.
Then came Campana's instant impact to extend Miami's unbeaten run to nine games after a night where little had worked for Gerardo Martino's team.
Campana had only been able to enter because a concussion substitution for D.C. allowed Miami coach Gerard Martino to make one more change, and he conceded that his team had barely deserved the win.
Sluggish
"I think this game should have been a 0-0 draw. We weren't sharp in this match but I don't want to take away merit from all the good things the opposition did, especially defensively...we weren't good in our build-up play," he said.
"(The win) was the product of an individuality. A minute earlier Drake had saved us and we could have lost. We were very sluggish, we lacked dynamism in our movement," the Argentine coach said.
In the "Hudson River derby," New York City FC emerged triumphant over the New York Red Bulls at Citi Field after Algerian Mounsef Bakrar grabbed the 64th minute winner.
Italy international Federico Bernardeschi scored a hat-trick for Toronto FC as they crushed Montreal 5-1 in their all-Canadian clash.
Diego Rossi, Christian Ramirez and Jacen Russell-Rowe were on target for defending champions Columbus Crew as they won 3-1 at the Chicago Fire.
Western Conference leaders Real Salt Lake trailed 3-2, with five minutes of regulation remaining in their Rocky Mountain derby at home to the Colorado Rapids, but sensationally struck three late goals to win 5-3.
Cristian Arango levelled in the 85th minute, with his second of the night, before Andres Gomez put RSL ahead, also giving himself a brace, before Anderson Julio added the fifth deep in stoppage time.
Hungary international Daniel Gazdag scored twice for the Philadelphia Union in their 3-0 win at the New England Revolution.
Phil Neville's troubles at Portland continued with the English manager seeing his team slump to their seventh loss in 14 games after a 2-1 loss at Minnesota.
Portland had led 1-0 but the home side, managed by former Manchester United coach Eric Ramsay, took the points after an 82nd minute winner from South Korean Jeong Sang-bin.
