The visitors were on course to take victory before a second-half red card preceded a collapse.
Both sides went into the game out of form but it was Ipswich who looked set for victory before handing Leeds the chance to snatch the game.
First, Ibrahima Sonko sent a weak header back towards Alex McCarthy, leaving the keeper no choice but to handle outside the area. He was rightly sent off by Geoff Eltringham and soon after Robert Snodgrass poked home from two yards after another error from Sonko.
Luciano Becchio sealed the points for Simon Grayson's men by firing into the bottom corner after the 90-minute mark.
Leeds move up two places to ninth and are now just a point off the playoffs, while Ipswich are just above the bottom three, four points clear of Nottingham Forest.