Wednesday led 1-0 at the break, but they wilted in the second half as Ipswich captain Luke Chambers secured his side’s first win in four matches to keep their promotion hopes well and truly alive.
The Suffolk side had to come from behind after Lee gave the visitors a surprise half-time lead.
But Championship top scorer Daryl Murphy equalised with his 19th of the season before Chambers burst in at the far post to score an even better header to claim all three points.
It was no more than Ipswich deserved as they struck the woodwork twice and always looked more likely to add to their tally.
A cagey opening burst into life on the quarter-hour mark when Murphy rifled his shot across goal and just wide. Five minutes later, it was the visitors who took the lead slightly against the run of play.
A mix-up between Ipswich centre-back Christophe Berra and his keeper Bartosz Bialkowski saw the ball pop off the chest of the latter and into the path of Lee, who placed the ball into the empty net.
Ipswich looked to hit back straight away and Murphy’s run at the heart of the visitors’ defence ended with a powerful drive that Kieran Westwood saved. Wednesday came close to doubling their lead on the half-hour mark following a fantastic challenge by Sam Hutchinson on Teddy Bishop. Will Keane teed up his strike partner Stevie May but he screwed his shot wide of the far post, while at the other end Murphy’s header hit the post.
But the Town No 9 did not have to wait long after the restart before equalising with another header. Only seven minutes of the second half had been played when he flicked Freddie Sears’s precise cross past the diving Westwood.
The winner came as Chambers met Kevin Bru’s cross to rifle a header into the corner.
Ipswich: Bialkowski, Chambers, Smith, Berra, Parr, Ambrose, Bishop (Bru 57), Skuse, S Hunt (Mings 46), Sears (N Hunt 86), Murphy. Unused substitutes: Gerken, Anderson, Tabb, Clarke.
Sheff Wed: Westwood, Vermijl (Buxton 66), Lees, Dielna, Mattock, McGugan (Nuhiu 66), Lee, Hutchinson (Filipe Melo 59), Helan, May, Keane. Unused substitutes: Palmer, Maghoma, Bus, Kirkland.
Referee: S Attwell (Warwickshire).