United trailed to Vladimir Gadzhev's goal, but three excellent second-half strikes from Kevin van Veen, Neal Bishop and Hakeeb Adelakun sealed victory.
The result meant Scunthorpe finished the season third in League One and they will take on the sixth-placed Lions on Thursday, May 4 (7.45pm at the New Den) and Sunday, May 7 (6.30pm at Glanford Park).
Scunthorpe manager Graham Alexander had made four changes to the side that emerged as 2-1 victors over Swindon last Saturday.
Jordan Clarke, Sam Mantom, Duane Holmes and Kevin van Veen all came into the starting 11, at the expense of Scott Wiseman, Jamie Ness, Stephen Dawson and Ivan Toney.
United started the game brightly and, within the first five minutes, van Veen had an opportunity to chip the ball over Lee Burge, but the Sky Blues keeper did well to block the effort with his body.
Josh Morris went close 15 minutes in and, after good work from Neal Bishop in the centre of the pitch, he set Morris up for a piledriver, but Burge parried it away.
Scunthorpe were piling forward and putting Coventry under immense pressure, with Mantom going close from a similar distance to Morris’ effort a minute or so prior.
The away side continued to live dangerously, as van Veen and Morris both had good opportunities straight after Mantom’s shot from distance. However, on both occasions, blocks from the Coventry defence prevented an opener.
The game died down for the next ten minutes, until van Veen’s flicked header sent Holmes down the wing on 35 minutes, before he crossed low to Paddy Madden, but his shot was somehow scrambled away.
Completely against the run of play, it was the visitors who took the lead in the 36th minute. United only half-cleared a cross from the left, before Vladimir Gadzhev picked the ball up, and sent a deflected effort past Joe Anyon.
The goal would be the last major chance of the first half, with the Iron wondering how they were losing at the break.
United started the second half much like they did in the first, on top. They then found their equaliser six minutes in, as van Veen picked the ball up before cutting inside and curling in a wonderful goal to level the score.
The Glanford Park faithful thought they’d seen Holmes score the Iron’s second a few minutes after the equaliser, but his run into the box saw his effort hit the side-netting.
Madden was next to try his luck after van Veen won yet another header, but the Irishman’s curled effort went narrowly, despite having Burge scrambling.
Coventry started to settle down over the course of the next 15 minutes, and were playing confidently for a team whose relegation to League Two had already been confirmed.
The away side almost capitalised on their good spell when George Thomas got on the ball in the Iron’s box, before unleashing a curled effort destined for the top corner, but Anyon somehow clawed it out.
United went ahead in 84th minute, and it was another memorable strike, this time from Neal Bishop. Madden, Craig Davies and Mantom were all involed, with the latter laying it into the path of Bishop, who took one touch before firing it passed Burge.
The home side weren’t finished yet, though. Substitute Hakeeb Adelakun dribbled passed two Coventry defenders before firing into the corner of the net from 25-yards out, making it 3-1.
Davies had a pop himself in the dying moments, but Burge held on at the second attempt. That would be the final opportunity of a great game.
Scunthorpe United: Anyon, Wallace, Mirfin, Madden, van Veen (Davies, 75), Morris (Adelakun, 75), Bishop, Mantom, Holmes, Townsend, Clarke (Sutton, 81).
Substitutes not used: Watson, Dawson, Toffolo, Toney.
Coventry City: Burge, Willis, Turnbull, Bigirimana, Lameiras, Jones (K. Thomas, 64), Gadzhev, Tudgay, G.Thomas (Folivi, 87), Dion Kelly-Evans, Camwell.
Substitutes not used: Charles-Cook, Reid, Devon Kelly-Evans, Shipley, Thompson.