Dajome's goal came in the 82nd minute after Cincinnati (7-7-6, 27 points) squandered a golden chance less than a minute before to make it a two-goal game.
It was Cincinnati's fourth straight draw.
Vancouver (7-9-4, 25 points) raced down the field and second-half substitute Tosaint Ricketts cut the ball back to Dajome. He found a small window between goalkeeper Roman Celentano and the post to tie the game.
It came only a few moments after Cincinnati's Sergio Santos found himself inside the box, but put a shot directly into the keeper's chest.
Celentano finished the game with two saves.
Cincinnati got off to a quick start with a goal by Alvaro Barreal in the third minute. Brenner found Barreal outside the box. His first two touches took him past two defenders and he then slipped a shot into the bottom right corner.
Vancouver would answer less than two minutes later. A failed clearance attempt landed at Dajome's feet and he sent a hard, low cross across the mouth of the goal. The ball fell to an onrushing Ryan Gauld, who was able to tap it in to tie the game.
Brenner picked up his second assist of the half after cutting through the defense and riding challenges before slipping a through ball for Brandon Vazquez. He finished calmly for his 10th goal of the season.
Vancouver had a scary moment around the 35th minute when a long ball by Cincinnati threatened the goal. Whitecaps goalkeeper Cody Cropper went up to clear the ball but collided with Javain Brown and flipped through the air before landing awkwardly.
Brown was substituted off while Cropper stayed down for a while but continued. He was eventually subbed off for MLS debutant Isaac Boehmer.
Cincinnati earned a free kick just outside the box after Tristan Blackmon got called for a handball in the 72nd minute. Barreal curled the ball in and Boehmer had to elevate to redirect it over the crossbar for his first career MLS save. He finished the game with three saves.