The draw dealt another blow to Hull's promotion hopes.
Ipswich midfielder Leadbitter had just converted a 67th-minute penalty when he pounced on a headed pass from half-time substitute Lee Martin three minutes later and arrowed an unstoppable half-volley past motionless Hull goalkeeper Vito Mannone into the top corner.
Leadbitter's strike stunned most in a crowd of 17,625 at the KC Stadium after the home side, who have drawn their last five matches, had taken a two-goal lead courtesy of Robbie Brady's deflected shot and Robert Koren's superb finish from the edge of the penalty area nine minutes after the interval.
Winger Brady, on loan from Manchester United, returned for Hull in place of Mclean, while Jason Scotland was back in Ipswich's starting line-up.
Scotland's strike partner Michael Chopra blasted wide from 30 yards in the opening minute and at the other end Ipswich goalkeeper Alex McCarthy held Corry Evans' angled drive from the edge of the penalty area.
Neither side created another chance until Hull took a deserved lead in the 17th minute.
Tigers striker Matty Fryatt slipped a pass inside on the edge of the area from the right and Brady's low shot took a deflection, wrong-footing McCarthy, on its way into the bottom corner.
Ipswich duo Adam Drury and Jay Emmanuel-Thomas, twice, were wayward with long-range shots as the visitors went in search of an immediate response.
But Hull threatened to double their lead in the 23rd minute when Fryatt's effort was blocked by Ipswich defender Damien Delaney and Brady headed Andy Dawson's subsequent corner just wide with McCarthy well beaten.
Brady was presented with another golden chance to head home from another corner, this time from Robert Koren, but again the young Irishman was unable to hit the target.
Ipswich began the second half on the front foot but Hull snatched a second goal through Koren in the 54th minute.
Substitute Mclean, on for the injured Brady at the start of the second half, provided a measured headed pass from the right and retired Slovenia international Koren rifled a 20-yard shot into the bottom corner.
But Ipswich hit back with two goals in three minutes to give the game a totally different complexion.
First Leadbitter slammed home from the penalty spot in the 67th minute following Mclean's foul on Tommy Smith in the area.
Leadbitter then completed the comeback in spectacular style, crashing home midfield partner Martin's pass on the half-volley from 20 yards.
Both sides went in search of the winner. Emmanuel-Thomas blazed a shot over the crossbar and Hull midfielder Paul McKenna volleyed inches wide soon after.
Scotland and Koren threatened to snatch the points for their respective sides with long-range efforts in the closing stages, but the points were shared with fast-improving Ipswich having lost just one of their last eight matches.