McKenna’s men had not won in their previous four games as they failed to take full advantage of Leeds’ faltering form at the business end of the season.
With a 2-1 victory over Coventry on Tuesday, Ipswich made significant progress towards their first Premier League appearance since 2002.
With one game remaining for both teams in the Championship, the Tractor Boys pull three points clear of Leeds in second place.
Ipswich, who visit Huddersfield on Saturday—who are all but relegated—need just a point to secure promotion.
To have any hope of finishing in the top two, Leeds, who do have a stronger goal differential than Ipswich, must defeat Southampton at Elland Road.
Kieran McKenna, a former Manchester United coach, is leading Ipswich to the verge of consecutive promotions.
“It’s another emotional night and we have had a few of them,” said McKenna.
“It’s a great night to enjoy in front of the supporters. We know the significance of tonight will not be determined until Saturday.
“To be on 93 points with a game to go is an incredible tally and credit to the boys.
“I never thought this could unfold so quickly. I came here because of the ambition of the club. The journey has accelerated, I have to say.”
McKenna’s men had not won in their previous four games as they failed to take full advantage of Leeds’ faltering form at the business end of the season.
But they righted the ship just in time with a precious victory over the FA Cup semi-finalists.
However, Ipswich’s nerves showed during a tense second half and Haji Wright’s powerful effort flew through the grasp of Vaclav Hladky.
Coventry were only level for five minutes as Cameron Burgess fired in at the near post to spark jubilant scenes among a packed out away end.
Those celebrations were repeated at full-time with Ipswich closing in on a £200 million bounty ($251 million) by making it back to the English top flight.
Leicester have already booked their place back in the Premier League as Championship winners after a 3-0 win at Preston on Monday.
