Kukushkin, ranked 59th in the world, has never been past the third round at the All England Club, but the Russian-born Kazakh showed few signs of nerves against the world No 3.
Murray arrived to a standing ovation from the expectant home crowd and the Scot could be forgiven for the spring in his step, after following up his most successful season on clay with the title at Queen’s Club.
Boosted this year by the addition of Jonas Bjorkman to his coaching team, which already boasts Amelie Mauresmo, Murray has added more aggression to his game and is now perhaps the greatest threat to Novak Djokovic defending his crown.
Kazakhstan’s Kukushkin held his own with some consistent serving and heavy ground strokes throughout the contest, but the Scot eventually broke him down in front of a??sun-baked crowd with some sizzling play to come through in two hours and 12 minutes.
“It was a tough match. I made it hard for myself at the end of the second set,” Murray said.
“There’s still work to be done for me, but I felt my opponent played very well. He made it very uncomfortable for me, so credit to him.
“I was glad to get it done in three sets because it was very hot out there.”
The two-time Grand Slam champion will play Dutchman Robin Haase next after the Dutchman beat Alejandro Falla from Colombia 6-2 3-6 6-4 6-2.
As the mercury soared to 30C at the All England Club, Murray avoided being dragged into a draining battle.
He took the first set in clinical fashion and raced into a 5-2 lead in the second.
However, a lapse in concentration allowed Kukushkin, who was starting to play with more aggression, to reel off four consecutive games.
The Kazakh wasn’t able to press home his unexpected advantage and Murray broke back to force a tie-break that he took with ease.
Murray then stepped up his level again to land the decisive break midway through the third set.