There were chances for City to do it without relying on the result at Prenton Park. Andy Dawson and Nick Barmby both had free kicks on the edge of the area that they couldn't find the target with.
Dawson also had a great chance arriving on the left side of the area but put his shot the wrong side of the post, after Ian Ashbee earlier had a chance for a captain's goal but failed to convert a cross at the back post.
The best move of the half was for Junior Lewis after Ryan France played him in with a through ball, but the ex-Swindon midfielder poke his shot just wide.
The visitors were doing their best to deny City any celebrations. Boaz Myhill twice saved Rory Fallon headers, while Brian Howard had a great long-range effort that flew just wide.
Goalkeeper Rhys Evans had to improvise to tip a looping ball over from Craig Fagan 25 yards out, before Peter Taylor signalled his intentions to go all out for the win by bringing on Kevin Ellison and moving Stuart Elliott forward into a three-man attack.
This was followed minutes later by the goal opening up for Ian Ashbee, but his 20-yard shot was going wide before ricocheting out for a corner.
City were desperately trying to scramble the ball in but were unable to make the vital touch.
Swindon were playing their part in the drama, with Rhys Evans charging out at his defender David Duke to berate him after the ball had gone for a corner. The two pushed each other and had to be separated by other players before any punches were thrown.
Back to football and the best chance came at the end of three minutes stoppage time. Seconds earlier, news was filtering through that Tranmere's game had finished goalless, but City could have sealed it with a goal themselves. Andy Dawson's corner wasn't caught by Evans, and Leon Cort fell as the 'keeper tried to recover and take the ball from his feet. The referee pointed at the spot, and Craig Fagan - who had scored two penalties from two since signing for City - was given the job of kicking Hull City into the Championship. He side-footed it at a decent height to the goalkeeper's right, and he parried it out. The rebound came out to Kevin Ellison, but the final whistle was blown immediately after the save.
There was then a moment before Tigers manager Peter Taylor ran on the pitch with his arms in the air, and the PA confirmed what he knew with the announcement of Tranmere's score resulting in City's promotion.
City line-up (4-4-2): Myhill; Stockdale (Joseph 78), Cort, Delaney, Dawson; France (Price 45), Ashbee, Lewis (Ellison 66), Elliott; Fagan, Barmby.
Un-used subs: Duke, Hessenthaler.