The Tractor Boys needed to win to keep their play-off chances alive, and headed into half-time level with already-promoted Burnley.
However, 10 minutes after the break the home side went ahead as Kightly grabbed his third goal in as many weeks - and it proved to be the winner as the Clarets secured the double over Ipswich.
Newly-promoted Burnley began with the intensity expected - Kieran Trippier finding Danny Ings, who nodded down for Scott Arfield, his first-time effort blocked by Christophe Berra after just two minutes.
And in the 11th minute the energetic Trippier again found Ings - the striker's instinctive flick to Ashley Barnes proving to be just inches too long.
A clear-cut opportunity still failed to arrive, though Paul Green had an opportunity to test Tom Heaton in the 14th minute but his tame effort failed to trouble the Clarets goalkeeper.
Ipswich then almost took an unlikely lead through centre-back Tommy Smith, his header superbly cleared off the line by Trippier.
That ramped Sean Dyche's men into action and on the half-hour mark Arfield met Kightly's teasing cross but could not direct it goalwards.
The visitors responded and should have gone ahead in the 41st minute when Frazer Richardson blazed over from 10 yards out with the goal at his mercy.
Almost instantly, Ings found himself on the corner of the box and the Burnley hitman produced several stepovers before firing agonisingly into the side-netting just before half-time.
The deadlock was broken in the 54th minute thanks to Kightly's second goal of the week.
Barnes slipped through Ings and although Dean Gerken denied the frontman his 21st league goal of the season, Kightly was on hand to tap-in to an empty net.
With the home crowd in full voice, the hosts strived to double their lead and came close shortly after. Ings did well to find space from 25 yards out before unleashing a half-volley which whistled agonisingly past Gerken's right-hand post.
In the 65th minute, substitute Junior Stanislas was immediately involved but the attacker failed to pounce on Dean Marney's long ball.
Eight minutes later Burnley thought they had doubled their lead after Marney's cross to Ings saw the striker's outstretched effort strike the bar.
Ings was again involved moments later as he looked to play through Stanislas, only a fine tackle from Paul Green denying him.
But Ipswich came back and almost levelled on 80 minutes as Paul Taylor's free-kick was clawed from the top corner by Heaton to hand Burnley all three points.