Sears arrived early at Portman Road to sign his long-term contract before breaking the deadlock in the 66th minute.
David McGoldrick added his name to the scoresheet five minutes later as Town finally made sure of the triumph – to maintain their unbeaten start to the season – after a closely fought opening hour which had defences well and truly on top.
Burnley, yet to taste victory on their return to the Championship, almost took the lead after just seven minutes when Michael Kightly wriggled past Luke Chambers.
After the home defence failed to clear the danger, the rebound fell back to the winger and his shot cannoned off the far post and into the arms of relieved Ipswich goalkeeper Bartosz Bialkowski.
In a poor opening half an hour, George Boyd fired over from the edge of the area and Chambers had a shot deflected just wide after the Ipswich skipper combined well with Arsenal loanee Ainsley Maitland-Niles.
Sears fizzed a drive straight at Tom Heaton shortly after the half-hour mark after latching on to a mistake from Burnley right-back Tendayi Darikwa, but it was the Clarets who ended the first half in the ascendancy.
A good counter-attack involving Boyd and Kightly led to Jelle Vossen shooting straight at Bialkowski when he should have done better before David Jones’ wicked inswinging free-kick narrowly missed the top corner.
The second half continued to be a little flat, with high-quality football at a premium, substitute McGoldrick heading over Maitland-Niles’ cross the only half-chance of a drab first quarter.
The match finally thrust into life in the 66th minute when an incisive attack saw Maitland-Niles feed Brett Pitman down the right and his low cross was turned in by Sears.
Five minutes later, the lead was doubled when McGoldrick was allowed a free header and found the bottom corner after Maitland-Niles’ deep corner.
The impressive Jonathan Douglas fired a speculative volley just over the far post as Burnley were left shell-shocked.
The visitors finally showed some life as the game neared its conclusion, with Ben Mee firing a shot just wide of the far post and Michael Keane’s fierce header being pushed away Bialkowski.
But Ipswich held on to claim what proved eventually to be a comfortable win while Sean Dyche’s men remained winless following a poor start to the season which has brought league draws with Birmingham and Leeds and a Capital One Cup defeat at Port Vale.