Murray has found it almost impossible to get the better of Djokovic over the last three years and had lost the Australian and French Open finals to the world number one this year.
But the 29-year-old, beaten in 13 of his last 15 meetings with Djokovic, no longer has to worry about ending that frustrating streak after the Serb was condemned to his earliest Wimbledon defeat for eight years by American 28th seed Sam Querrey.
Djokovic's humiliating loss was taking place on Court One at the same time as Murray was maintaining his serene progress just yards away under the Centre Court roof.
Asked about Djokovic's exit, Murray refused to admit it was a help to his title ambitions, but conceded he was surprised to see the Serb bow out.
"Right now everyone expects Novak to win every match. He almost found a way to get back into that one today," Murray said.
"I need to reach the final for that result to have any bearing on my performance. I've got some tough opponents in my half of the draw, including the next round."
The Scot has now reached the fourth round in his last 22 consecutive Grand Slams as he aims to become the first British man to win multiple Wimbledon titles since Fred Perry.
- Peaking -
===========
Having also brushed aside Liam Broady and Lu Yen-Hsun without dropping a set in the first two rounds, Murray appears to peaking just in time for the latter stages of the tournament.
Murray had only failed to make the fourth round once in his 10 appearances at Wimbledon and world number 67 Millman never threatened to become the first Australian to beat the Scot in 18 tour-level attempts.
But it was Murray who was in business-like mood right from the start.
A pair of breaks ensured Murray cruised through the first set before rain sent the players back to the locker room.
Murray hadn't dropped more than four games in a set in this year's tournament, but when they returned under the closed roof that record came to an end before he edged a tight second set.
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