The fitting farewell for loose forward Scott Higginbotham and captain Samu Kerevi looked unlikely with the Reds trailing 21-5 after 23 minutes following a sluggish start.
But the hosts clawed back the deficit and secured just their sixth win of the season.
Higginbotham's first-half try, following good work by Kerevi and winger Jock Campbell, made him the first forward to notch 40 Super Rugby tries.
His effort came either side of tries to Blues' pair Tanielu Tele'a and Augustine Pulu after captain Blake Gibson opened the scoring after just three minutes.
Taniela Tupou's close-range effort after a mountain of pressure inside the Blues' 22 and a penalty by Hegarty ensured the margin was six points at halftime.
The Reds then hit the front three minutes into the half when Hegarty scored before Pulu's second of the night on the back of a Tupou penalty put the New Zealanders clear again by six points.
A yellow-card to Dalton Papali'i reduced the visitors to 10 men but it wasn't until Papali'i had returned to the field that the Reds swept the ball out to the left wing for Higginbotham to go over for his 41st Super Rugby try.
Kerevi batted away speculation over his future after the match, saying his emotional response to the win had more to do with the Reds snapping a 15-game losing streak against New Zealand opposition.
A TMO review to deny a possible third try to Pulu when the Blues led 28-22 midway through the second-half proved crucial in the opinion of Blues coach Leon Macdonald.
Officials ruled the halfback failed to properly release the ball after being tackled before diving over the line.
"I just can't see why it wasn't a try," a frustrated Macdonald said.
"Referee found a way, so yeah."
The Blues finish their season against the Hurricanes in Wellington next weekend while the Reds have a match against Australian conference leaders the Brumbies in Canberra.