Fraizer Campbell's goal was Hull's third in 15 second-half minutes
Joe Bryan's injury-time strike saw Bristol City keep alive their slim play-off hopes as they salvaged a draw with Hull in a thriller which they twice led by two goals.
Harry Wilson curled Hull ahead, but Marlon Pack's 25-yard shot and a Famara Diedhiou strike and header made it 3-1.
Fikayo Tomori headed Hull's second before Bobby Reid made it 4-2.
Strikes by Wilson, Abel Hernandez and Fraizer Campbell in a crazy 15 minutes saw Hull lead, only for Bryan to level.
But despite the euphoria of the late drama during 10 minutes of added time at Ashton Gate, the Robins are 10th in the table, three points adrift of Millwall in sixth with just two games remaining.
That gap looked certain to be just a point after City's sensational response to Wilson's early opener.
The hosts looked sharp and lively and created several chances before Pack's rasping effort and Diedhiou's close-range shot within three minutes of each other settled the nerves.
Famara Diedhiou has 14 goals in 34 appearances for Bristol City this season
Diedhiou scored his second with a fine glancing header from Reid's cross after the break.
On-loan Chelsea defender Tomori's downward header - which went in off goalkeeper Frank Fielding and was later credited as an own goal - seemed to be of little consequence when Reid ran onto Diedhiou's pass to restore Bristol City's two-goal advantage with his his 20th league goal of the season.
However, a Wilson free-kick squirmed past Fielding to make it 4-3 and substitute Hernandez levelled with a deflected Kamil Grosicki cross for the eighth goal of the afternoon on 80 minutes.
Campbell's left-foot finish from another Grosicki cross seemed certain to have secured victory for Hull, only for left-back Bryan to curl home a brilliant 93rd-minute equaliser.
Hull are now certain of Championship survival, having lost just three times in 12 games.
Bristol City head coach Lee Johnson:
"We are all a bit shell-shocked. Having played well in the first half, we got ourselves 4-2 up and in a great position to take the points we needed.
"Our attacking play deserved even more goals but some of the defending was schoolboy errors.
"We will keep fighting, but obviously we now need a storming finish to the season and hope things go our way.
"Perhaps we lack enough leaders on the pitch. Players can be divided into followers, standard-setters and leaders and we need more to graduate from the second of those categories to the third."
Hull manager Nigel Adkins:
"We wanted to be in control of our own destiny today and it is great to achieve safety on the back of a positive result.
"Again the players have shown great character and a real sense of togetherness to twice come back from two goals down. Some of our attacking play was outstanding.
"Of course, I am not happy to concede five and there were some really poor ones from our point of view. But overall we have come out of a brilliant game to watch, having not been beaten by a team desperate to get into the play-offs.
"Now we want to continue building on our recent form in the last two games."
