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The Australian eventually prevailed 3-6 6-1 7-5 6-7 (3) 7-5 in three hours and five minutes at a rowdy Court Three crowd.
In trademark Kyrgios fashion, the world number 40 was involved in a number of prickly chats with line judges and spectators, but a mixture of 30 aces and an array of glorious winners sent him into round two.
Jubb started impressively in his second main draw appearance at the All England Club and claimed a decisive break in the eighth game of the first set to clinch the opener in 23 minutes.
Kyrgios, who had already produced one under-arm serve, smashed a tennis ball out of the court to threaten a round one implosion but regained his cool and broke twice in the second before he edged a tight third.
By this point the 27-year-old had been involved in regular talks with a number of line judges and spectators.
At one stage, he turned to the umpire and was heard saying about some spectators: “I don’t go to their nine to five and start clapping when they’re scanning s*** at a supermarket do I? Go ‘boo, well done, you can’t scan that thing for s***’…You should remove them from the crowd.”
York-born Jubb did his best to not interact with his opponent and showed more than enough of his talent with numerous wristy forehand winners forcing a decider after a tie-break.
When Kyrgios broke in the sixth game of the fifth set, it appeared the Aussie would coast home but Jubb fought back when his rival had the chance to serve for the match and then held to get proceedings back on serve.
A 134mph ace helped Kyrgios to a big hold at 5-5 and he progressed with his second match point to break again, which brought an entertaining round one clash to an end.
Afterwards, Kyrgios said in his on-court interview: “He played some exceptional tennis at times and the crowd were pretty rowdy today.
“A couple of people in the crowd were not shy of criticising me, so that one was for you – you know who you are.
“I thought I was going to go down there and it would have been a tough, tough loss to take so I am just happy to be through.”