The British number one eventually triumphed 7-5 6-7 6-3 6-4 against a man who had not won a game against him the last time they played on grass.
It was a performance which will have raised a few doubts and maybe also lowered a few expectations on Murray.
But Murray got the job done in the end and admitted: “It was a tough match. He served great for three sets and made it difficult for me. I didn’t return as well as I liked. There were a lot of big points and it is good to have them early in the tournament.
“He played very aggressively and he doesn’t give you rhythm. I didn’t hit my groundstrokes as well as I could but I was happy to come through.”
It was not the best of first sets from Murray, even though he did break Kendrick’s serve in the first game of the match when the American understandably appeared to be troubled by nerves.
Murray threatened to breeze past a player who had never beaten anyone in the top 20, but Kendrick took advantage of a double fault from the Scot to claw back the break in the eighth game.
Suddenly, the American’s flat forehand and big serve was starting to give Murray problems.
A wild forehand wide of the tramlines from Kendrick secured the crucial break in the 11th game and allowed Murray to clinch the set.
Kendrick was much more competitive after switching his game plan to keep the ball away from Murray’s dangerous backhand.
When the set went to a tie-break it was the American, aided by a Murray double fault, who dominated proceedings, a spectacular forehand clinching the breaker 7-3 to tie the match at one set each.
There was an air of apprehension on Centre Court until the match took a decisive turn in the sixth game of the next set when Kendrick threw in two uncharacteristic double faults, one of them courtesy of a foot fault, in the sixth game.
It allowed Murray to seize the set and it was clear he was gradually grinding down the resolve of his opponent.
The crucial break came in the fifth game of the fourth set, Murray finally asserting his authority to take his place in the second round against Latvia’s Ernests Gulbis and send a collective sigh of relief around SW19.
Earlier Juan Martin Del Potro did a passable impression of absent defending champion Rafael Nadal.
Fifth seed Del Potro has assumed Nadal’s position in the draw following the Spaniard’s withdrawal with a knee injury, and turned in a suitably impressive display in beating Arnaud Clement in straight sets on Court One.
The Argentinian raced to a 6-3 6-1 6-2 victory in just 97 minutes to set up an intriguing second-round clash with former champion Lleyton Hewitt.
“It was easier than I was thinking before the match,” admitted Del Potro, who pushed Roger Federer all the way in the French Open semi-finals recently, but had not competed on grass since losing in the second round at the All England Club 12 months ago.
“Clement is a good player. He knows how you play on this surface and reached the quarter-finals last year. I prefer hard courts for sure, but I want to learn play this surface.
“Now I have a very good player in front of me, but I have my weapons, I have my game, and I am confident with that and try to beat him.”
Hewitt, the 2002 champion but unseeded this year, also only dropped six games in thrashing American Robby Ginepri 6-4 6-1 6-1 but knows it will be a different story against Del Potro. “It’s gonna be a tough match,” said the Australian. “He’s a class player. He was only a couple of points from maybe winning the French Open a couple of weeks ago. It’s going to be a good challenge.”
Sixth seed Andy Roddick maintained his record of never having lost in the first round in nine visits to Wimbledon, but needed four sets to see off former junior champion Jeremy Chardy of France.
Nikolay Davydenko, the 12th seed, enjoyed a comfortable win over British wild card Daniel Evans, while 24th seed Tommy Haas beat Alexander Peya of Austria in four sets in a match held over from Monday evening.
There were also victories for 20th seed Tomas Berdych over Britain’s Alex Bogdanovic, 23rd seed Radek Stepanek over Alejandro Falla and 16th seed David Ferrer beat Kevin Kim in four sets.
Fernando Gonzalez, the number 10 seed, enjoyed a straight-sets win over Teimuraz Gabashvili, but 33rd seed Nicolas Kiefer was beaten in three sets by France’s Fabrice Santoro.
Meanwhile Marat Safin saw his final Wimbledon brought to a surprisingly early conclusion with an opening-round defeat to American qualifier Jesse Levine.
The Russian 14th seed, who intends to retire at the end of the year, was beaten 6-2 3-6 7-6 (7/4) 6-4 in two hours and 16 minutes on Court 18.