The third seed and 2013 champion looked on course to cruise through when the wheels came off his serve.
Murray, among the favourites to clinch a second Wimbledon title this year, was some way from his best in an inconsistent first round display.
The 28-year-old Scot, who now faces Holland’s Robin Haase in round two, has been working on a more aggressive style of play with the help of new coach Jonas Bjorkman, but opportunities to dominate points were few and far between.
Kukushkin dictated the direction of the match with his dangerous, but inconsistent forehand, and Murray at times appeared at the mercy of his opponent’s momentum.
“For me it’s a bit frustrating because you obviously want to go out there and perform as best you can, whereas today I didn’t feel like I was able to do that because of the way that he was playing,” Murray said.
“He was hitting the ball this high (very low) over the net and so flat and down the line.
“It’s very difficult to dictate points when your opponent’s playing like that.”
Murray added: “The way he played just made it extremely difficult to play offensive tennis.
“You just have to sometimes knuckle down and try to get the win.”