Substitute Brett Pittman headed a Cole Skuse chip forward over goalkeeper Adriano Basso 12 minutes from time just as Ashton Gate fans were starting to turn the heat up on their manager.
Robert Koren had fired Hull in front with a low right-footed drive after exchanging passes with Aaron Mclean on 56 minutes.
And when Millen responded by taking off strikers Jon Stead and Nicky Maynard on 62 minutes following four home matches without a goal he was roundly booed by disgruntled home fans.
However, it proved the right move as replacement Pitman and Ryan Taylor at last started to stretch a previous untroubled Hull defence.
Millen said: "I'm paid to make tough decisions at times and, while some of the fans didn't like the substitutions, they helped us draw the game.
"We needed some fresh legs up front and the whole team showed a great attitude after falling behind.
"We could easily have folded after Hull scored and the fact that we stormed back convinces me we shall be alright this season.
"Brett's goal has lifted some pressure off us. After we scored you could see there was more belief in our attacking play.
"Now we have to take that into Tuesday's home game with Reading. There has been no doubting the effort of the players and now we have something to build on."
Hull manager Nigel Pearson was unhappy with Pitman's goal, claiming midfielder Tom Cairney had been fouled in the build-up.
"My players are furious that we were not awarded a free kick and I can understand their frustration" he said.
"As a manager, all I am looking for is consistency from referees and their assistants. We didn't get that today and it cost us dear.
"We have defended brilliantly throughout the game, as has been the case in recent matches, and looked like holding on for another excellent victory.
"Instead, we are going home bitterly disappointed at not taking all three points, having scored a very good goal to get our noses in front."
Hull goalkeeper Basso was given a tremendous reception by home fans on his return to Ashton Gate, having spent five years as a Robins player and helped them win promotion to the Championship.
He had to make the best first-half save palming over a 10th-minute shot from Marvin Elliott, who also sent a header just over the bar.
Former England keeper David James looked suspect in Bristol's goal, spilling a Martyn Waghorn shot from 25 yards and a weak effort form McLean, which he should have dealt with comfortably.
The half-time whistle brought jeers from unhappy Bristol fans who by then had watched more than 400 minutes of football at Ashton Gate this season without seeing their team score.
The second half was an improvement. Basso saved well from Neil Kilkenny and after Millen's substitutions his side looked the more likely winners.
Source: Team Talk
Source: Team Talk