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The Bulgarian was matched shot for shot in a tight start to the meeting, but he managed to edge ahead of the Australian with a break in the sixth game.
Dimitrov then saved a break on his own serve before wrapping up the opener, and he carried his form into the second set with a break in the first game.
Saville struggled to cause many problems on his rival's serve, and Dimitrov's quality was clear as he found a second break of serve to take a 2-0 set lead.
The Australian displayed his battling qualities to save three break points early on in the third set, but his resistance did not last for much longer as Dimitrov continued to dominate to edge ahead once again.
Dimitrov needed just two of his three match points to complete the victory on Centre Court.