The champions seemed to have rediscovered their confidence after Tuesday's Champions League success and an early goal dissolved any lingering nerves, but once again their fans were biting their nails until the final whistle.
Bob Malcolm created the opening goal with a glorious pass through the home defence, perfect for Lovenkrands' pace, and the Dane sprinted into the box and drove the ball home under Alan Combe.
The Killie defence were screaming for offside, but Simon Ford appeared to keep him legal. Home boss Jim Jefferies took his protests too far and he was banished to the stands.
Killie tried to claw their way back into the match but failed to test the uncertain Ronald Waterreus.
They should have been awarded a penalty in the 27th minute when Malcolm seemed to handle the ball after Kris Boyd had knocked down, but referee John Underhill dismayed the home fans and players by waving play on.
Lovenkrands beat the offside trap again in the 31st minute and squared the ball unselfishly to Thomas Buffel, but Combe produced a breath-taking save to keep his side in the game.
The Gers grabbed a second goal two minutes before the break. Buffel picked up the ball in midfield after a Killie corner and carried the ball deep into enemy territory before picking out Lovenkrands at full tilt. He blasted high into the net from 12 yards.
Chris Burke had two chances to put Rangers on easy street before the break, but first shot wide before collecting the rebound from another Combe save, only for Ford to clear on the line.
The hosts pulled one back in the 61st minute thanks to some shoddy Rangers defending. Waterreus and Marvin Andrews seemed to hamper each other as Boyd and Steven Naismith lurked. Naismith picked up the loose ball and could have scored himself, but passed to Gary McDonald who could not miss from five yards.
Lovenkrands calmed the nervy Ibrox side in the 72nd minute when he completed his hat-trick after taking the ball off Buffel's toe when he poised score one of the goals of the season after twisting Ford and Combe inside out before the striker nipped in to score into the open goal from point blank range.
Boyd set up a grandstand finish as he bundled the ball home in the 82nd minute after the defence had failed to clear Stevie Murray's free-kick, but Rangers held on for an important win.