As an enthralling duel neared its conclusion the 21-year-old Muguruza was serving at deuce, 5-3 and thumped a deep drive that Poland's Radwanska scrambled back before stopping mid-rally to challenge after hearing shouts of "out" from her coaching team.
The Hawk-Eye screen showed Muguruza's shot had actually landed on the outer portion of the dusty baseline and even though the Spaniard's next shot was out, the point was already hers as Radwanska had put her fate in the hands of technology.
Radwanska glared towards her box, Muguruza punched the air in relief and seconds later was celebrating victory after swinging away a volley to end the thriller and set up a Saturday afternoon date with five-times champion Serena Williams.
It was an unusual conclusion to a match which had looked like being a quickfire win for Muguruza in her first major semi-final.
"It was a 50-50 decision but it wasn't a very good decision," Radwanska, beaten by Williams in the 2012 final, told reporters.
Muguruza, who had never been beyond the second round at Wimbledon, was just delighted the decision had gone her way, saying: "I heard some people were saying 'out, out' but I was just praying the ball was on the line."
NO NERVES
Playing the biggest match of her career, Venezuelan-born Muguruza began boldly, overwhelming Radwanska with her heavy hitting as she won the first set in 34 minutes.
If Radwanska had a Plan B it was not instantly apparent as she fell 3-1 behind in the second set with Muguruza in control.
But the 26-year-old Pole, a former world number two, finally began to extend the rallies, keeping the ball away from Muguruza's strike zone.
A stunning shift of momentum saw Radwanska win six games on the bounce with her clever placement provoking errors.
Muguruza, the youngest of the semi-finalists, never lost heart though, despite going down an early break in the decider, and after winning a tense service game at 2-2 she broke Radwanska and then held her own serve for a 5-2 lead.
There were understandable nerves as she served for the match at 5-3, not helped by a foot-fault, a double-fault and the Hawk-Eye drama, but a booming serve on match point forced Radwanska to spoon the ball into the air and Muguruza pounded it away.
"When I was 6-2 3-1 I thought, 'OK, wait, you're the only one that can lose this match'," Muguruza, the first Spanish woman to reach a grand slam final for 15 years, said.
"In the third set I lost the fear to win the match."
(Reporting by Martyn Herman; editing by Ken Ferris)
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