The home side took an early lead through Sears before an out-of-sorts Leeds equalised just before half-time.
The visitors improved after the restart and enjoyed a good share of possession but Ipswich created the best of the second-half chances with David McGoldrick hitting the crossbar with a delicate chip.
A bright start saw Ipswich take a ninth-minute lead when a driving run from Emyr Huws ended with him sliding the ball out to Grant Ward whose first-time cross was neatly volleyed home by Sears.
Ward almost added a second in the 16th minute when he caught Dallas in possession on the edge of his own area but fired a shot just wide of the upright.
The home side were in the ascendancy and more great work by Huws almost led to Jonas Knudsen scoring from close range but Ronaldo Vieira did well to block the goalbound effort before, from the resulting inswinging corner, Rob Green had to be alert to push over Huws' free-kick.
Out of nothing, Leeds equalised in the 42nd minute. Hadi Sacko's cross was flicked on by Chris Wood and Dallas got on the wrong side of Jordan Spence to fire the ball under Bartosz Bialkowski.
The equaliser led to an evenly-contested start to the second half with neither side giving an inch.
Leeds bossed possession but the pace of Sears remained a danger and the striker did well to beat sub Liam Bridcutt in the area but his dangerous low cross was turned away by Pontus Jansson.
Green palmed the ensuing corner out to McGoldrick whose delicate chip came back off the crossbar and Christophe Berra could only head the rebound at the relieved Leeds keeper.
McGoldrick again went within a whisker of restoring Ipswich's lead when Spence headed Kevin Bru's free kick across goal and the Town striker just failed to apply the final touch at the far post.
Some last-ditch defending again thwarted Sears and McGoldrick in quick succession as Ipswich once again raised their game.
The two home strikers were a constant danger and they combined brilliantly in the 77th minute.
McGoldrick's raking crossfield ball released Sears, who returned the compliment with a cross that Town's number 10 fired goalwards but Green was alert to parry the ball around his near post.