The last British woman to reach the quarterfinals was Jo Durie in 1984.
Garcia had beaten Konta, also in three sets, at Indian Wells in March but she is yet to beat a top-10 player at a Grand Slam and this time it was Konta's serve, and nerve, that came up trumps.
Next up is Romania's Simona Halep, the number two seed, who needs just one more win here to secure world number one status.
Feeling her error had been prompted by the out-call, Konta briefly protested but she quickly recovered and stormed into a 3-0 lead in the tie-break. Muguruza is probably the player least likely to wilt in a major final, but she has to get there first.
In her first four rounds she has shared the spotlight with Andy Murray but with the men's and women's singles now running on alternate days, she finds herself all alone in the full and burning glare of national expectation. The 26-year-old maintained she was not playing against a crowd (indeed, it will be on her side this time around) or a past experience, but another tennis player - and a top one at that.
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Speaking at the French Open last month, Garcia talked about the criticism she has faced and said: "For sure, it's always nice to see support from people around you and people you don't even know".
When Garcia ruled herself out of contention to play for France in the Fed Cup in April, by announcing she had a back injury after being selected against her wishes, Mladenovic together with fellow French players Alize Cornet and Pauline Parmentier each tweeted "LOL" nearly simultaneously.
Her level dipped in the second as French star Garcia's rose, and at 5-1 it looked a foregone conclusion. It's going to be a very interesting week. Konta's strategy is clear, she's meant to hit the ball early and maintain the depth dictating the points and moving her opponent.
Sixth seed Konta won 7-6 (7-3) 4-6 6-4 on Court One to reach her third Grand Slam quarter-final.