Dean Gerken was called into action shortly before the break when Ashley Barnes unleashed a powerful strike from long range, but the Ipswich keeper denied him.
Both sides looked lively at the start of the second half, but it was the hosts who managed to break the deadlock less than 10 minutes after the restart when Gerken parried a Luke Chambers shot away only for it to fall to Kightly for a simple tap in.
Daryl Murphy tried to force a quick equaliser for Mick McCarthy's side, but his 30-yard effort went well wide.
The hosts came close to doubling their lead with just over 20 minutes to go with a David Jones free kick, but the ball was eventually cleared after a scramble in the box.
Ings almost found the target a few minutes later when he tried to sidefoot the ball in from close range, but his finish clattered into the crossbar.
However, Tom Heaton had to remain alert late on when Paul Taylor almost forced the ball into the top net from a free kick, but the Burnley keeper made the stop.
Taylor proved a threat again in the final minute of the match, rounding two defenders before crossing in for Christophe Berra, who could only head wide.