Twice two goals behind, the Tigers roared back to lead 5-4 late on and were only denied victory by Joe Bryan’s equaliser deep into six minutes of stoppage-time.
Adkins said: “We wanted to be in control of our own destiny 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.
“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.”
Harry Wilson fired Hull ahead from just inside the area, but by half-time they trailed to goals from Marlon Pack and Famara Diedhiou, whose header on 53 minutes put the hosts 3-1 up. Goalkeeper Frank Fielding conceded a 56th-minute own goal when a header from substitute Fikayo Tomori hit a post and went in off him.
Bobby Reid made it 4-2, but Wilson beat Fielding at his near post with a 30-yard free-kick and substitute Abel Hernandez fired home from close range to level.
Fraizer Campbell converted a low cross on 84 minutes, but Bryan had the last word.
Bristol City: Fielding, Pisano, Flint, Baker, Bryan, Paterson, Smith (Taylor 84), Pack, O’Dowda (Brownhill 66), Diedhiou, Reid, Brownhill (Djuric 90). Unused substitutes: Wright, Steele, Eliasson, Kelly.
Hull City: McGregor, Aina (Tomori 44), Dawson, MacDonald, Kingsley, Larsson, Henriksen, Bowen (Grosicki 63), Irvine (Hernandez 63), Wilson, Campbell. Unused substitutes: Hector, Meyler, Toral, Marshall.
Referee: O Langford (W Midlands).