Kukushkin, ranked 59th in the world, has never been past the third round at the All England Club but the Russian-born Kazakh offered a stiff examination for Murray, who came through 6-4 7-6 (7/3) 6-4 on Centre Court.
Murray will now play Holland’s Robin Haase in the second round as he looks to add another triumph to the Wimbledon crown he won two years ago.
The British No 1 arrived to a standing ovation from the expectant home crowd and he could be forgiven for having a spring in his step, after following up his most successful season on clay with a fourth title at Queen’s Club nine days ago.
Boosted this year by the addition of Jonas Bjorkman to his coaching team, which already includes Amelie Mauresmo, Murray has added more aggression to his game and arguably poses the greatest threat to Novak Djokovic defending his crown.
Opportunities to demonstrate his more varied style, however, were few and far between against Kukushkin, who held his own throughout with some heavy hitting and a particularly destructive forehand.
Murray, however, stepped up at the crucial moments, starting in the opening set when he forced two break points at 5-4, before converting a third to move one set clear after 35 minutes.
The cushion seemed to relax the number three seed, who played more freely at the start of the second as a whipping forehand winner prompted an early break and a 3-0 lead.
A number of spectators, presumably satisfied their man was in control, took their leave at the change of ends but Kukushkin had other ideas, unleashing a hammering return to break back and trail 3-2.
Murray has been eager to assume more authority over his opponents in recent months but it was Kukushkin, and his forehand, that was dictating the direction of the contest.
It flew long to give Murray another break but soon found its range as Kukushkin won four games in a row, including two breaks, to serve for the set at 6-5.
Murray, however, dug deep to force a tie-break and the Briton, spurred on by the invigorated home crowd, made his quality count.
Racing into a 6-1 lead, Kukushkin’s momentum was lost and a backhand long allowed Murray to seal the tie-break 7-3 and take a two-set advantage.
Murray was back in the ascendancy thereafter and he enjoyed an excellent start to the third set as he immediately broke Kukushkin serve to lead 2-0.
His opponent, however, refused to lie down and it was left for Murray to serve out the match as he led 5-4.
The Scot’s concentration wobbled as a double fault offered Kukushkin two break points, but this time there was no comeback as a backhand wide sealed Murray’s hard-fought win in two hours and 13 minutes.