Wildcard Murray, the 2013 and 2016 champion, played some vintage tennis against Basilashvili but from 5-0 ahead in the third set he lost seven successive games before settling down to win 6-4 6-3 5-7 6-3
Defending champion Novak Djokovic began his quest for a sixth title with victory over British teenager Jack Draper on Monday but suffered an early scare as Wimbledon returned after a two-year absence on Monday.
Andy Murray, playing his first singles match at the All England Club for four years, also had a fright but delighted the home fans with a four-set victory over Nikoloz Basilashvili.
Djokovic, unbeaten at Wimbledon since 2017, was caught cold on a slippery Centre Court as wildcard Draper threatened a huge shock on his Grand Slam debut by taking the first set.
But Djokovic, bidding to equal Roger Federer and Rafa Nadal’s record of 20 Grand Slam titles, was unruffled as he moved through the gears to win 4-6 6-1 6-2 6-2.
Wildcard Murray, the 2013 and 2016 champion, played some vintage tennis against Basilashvili but from 5-0 ahead in the third set he lost seven successive games before settling down to win 6-4 6-3 5-7 6-3.
On a rain-hit day, twice women’s champion Petra Kvitova suffered a first-round loss to American Sloane Stephens while on the men’s side the day’s big casualty was French Open runner-up and third seed Stefanos Tsitsipas who was trounced by American Frances Tiafoe. Highlights of day one of the Wimbledon tennis championships on Monday (all times GMT):