After Jason Scotland had given Ipswich a first-half lead, an error from Smith allowed Leeds to poach an equaliser through Robert Snodgrass.
But, after former Ipswich defender Alex Bruce was sent off for a second yellow card, Smith was afforded the freedom of the Leeds penalty area and headed home the winner.
Smith was never meant to start the game, but turned out to be one of four changes made by Roy Keane when he had to replace Darren O'Dea who was injured in the warm-up.
Having seen a 4-1 lead turn into a 6-4 defeat against Preston on Tuesday, Leeds manager Simon Grayson was not shy in making changes to his side either and made four alterations to his starting line-up.
Smith proved his worth early on as he blocked Richard Naylor's goalbound header.
Neil Kilkenny, one of those recalled by Grayson, then failed to get a good connection to a Snodgrass cross, and Davide Somma narrowly failed to nip in to capitalise on a scramble as Leeds applied some early pressure.
It failed to tell, though, and the home side took the lead after 19 minutes.
Jake Livermore picked up the ball in midfield and, after running at the Leeds defence, slotted a perfect pass through to Scotland who rounded Shane Higgs and converted.
The former Wigan man looked to add a quick second but dragged a low drive wide, but, although Somma fizzed a 30-yard effort off target, Scotland's goal gave Town a half-time lead for the first time this season.
That lead was nearly wiped out after the restart as Bruce whipped a dangerous ball across Marton Fulop's goal, with three United players narrowly failing to connect.
Scotland should have made it two for Ipswich, though, when he sliced over from six yards, while Bradley Johnson wasted a chance for Leeds when he curled a free-kick wildly over from just outside the area.
Higgs then left the field with a hamstring injury, forcing Leeds to bring on Blackburn loanee Jason Brown, who was quickly in the action as he turned behind a Scotland effort.
Scotland was made to pay for his missed chances when Leeds equalised 13 minutes from time.
Smith and Gareth McAuley both jumped for the same ball and, after they failed to clear, Somma played in substitute Sanchez Watt who had the awareness to square for the waiting Snodgrass.
Leeds had the initiative at that point but they were quickly robbed of it as Bruce was dismissed for a second yellow card after one foul too many on the dangerous Andros Townsend.
And Bruce was made to pay for his indiscretion when, after Ipswich received a free-kick with eight minutes remaining, Smith was left unmarked by the Leeds defence and got on the end of Carlos Edwards' cross.