Mickelson, who is seeking a first title since winning the 2013 Open at Muirfield, defeated Australia's Marc Leishman 4&3 in their last-16 clash at Austin Country Club on Saturday.
And that means the 46-year-old has yet to be extended beyond the 15th hole so far this week after similarly impressive victories in the group stages of the £7.8million event.
Mickelson, who thrashed Ryder Cup team-mate JB Holmes 6&5 after beating Si Woo Kim 5&3 and Daniel Berger 5&4 to win group 14, was five up after 10 holes against Leishman, who survived a three-man play-off to emerge from his group.
A birdie on the 11th and a par on the 12th saw Arnold Palmer Invitational winner Leishman reduce his deficit to three holes, but the 33-year-old made a mess of the 15th and - with Mickelson in close - conceded the hole and the match.
"I'm certainly a little bit worried, because I know there's going to be a key match that's going to go down to the last few holes," Mickelson told PGA Tour Live. "And I'm not as comfortable on those holes as I'd like to be.
"But I love the fact that I'm able to be rested and ready to play, because I think it's helping me get off to a good start."
Mickelson will face Bill Haas in the quarter-finals after Haas beat fellow American Kevin Na on the 18th.
Spain's Jon Rahm, who has not trailed at any point in his four matches so far, was the first man into the last eight after thrashing American Charles Howell III 6&4.
And Rahm will face Denmark's Soren Kjeldsen for a place in the semi-finals after Kjeldsen, who beat Rory McIlroy in his first group match on Wednesday, defeated William McGirt 5&4.
On the other side of the draw, world number one Dustin Johnson remained on course to become the first player to win all four WGC titles with a 5&4 victory over Zach Johnson.
Johnson, who is seeking a third straight tournament victory, will face Sweden's Alex Noren in the quarter-finals after Noren overcame Brooks Koepka 3&1.
England's Ross Fisher holed a bunker shot on the 15th to seal a 4&3 win over two-time Masters winner Bubba Watson and set up a quarter-final with Japan's Hideto Tanihara, who beat Paul Casey 2&1.
Fisher's win is expected to be enough to take him into the world's top 50 on Monday and secure a first appearance in the Masters since 2012.
Quarter-final draw:
Jon Rahm (21) v Soren Kjeldsen (62)
Phil Mickelson (14) v Bill Haas (42)
Ross Fisher (47) v Hideto Tanihara (54)
Duston Johnson (1) v Alex Noren (8)
Round of 16 results:
Soren Kjeldsen (62) bt William McGirt (48) 5&4
Ross Fisher (47) bt Bubba Watson (13) 4&3
Jon Rahm (21) bt Charles Howell III (61) 6&4
Phil Mickelson (14) bt Marc Leishman (28) 4&3
Bill Haas (42) bt Kevin Na (46) 1 up
Dustin Johnson (1) bt Zach Johnson (44) 5&4
Hideto Tanihara (54) bt Paul Casey (12) 2&1
Alex Noren (8) bt Brooks Koepka (20) 3&1
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