Pegula has ground her way up the rankings over the past few years, culminating in her reaching a much-wanted Slam final.
It has not been easy – she has been asked questions for years about her quarter-final struggles, having previously reached the last eight of every major but failing to kick on in six attempts.
She split with long-term coach David Witt at the start of the year before struggling with injury, with a neck and back problem disrupting her clay-court season.
Pegula has also had little joy at the Slams, missing the French Open and losing in the second rounds of the Australian Open and Wimbledon.
She was superb against an off-colour Swiatek earlier in the week to put her quarter-final hoodoo behind her – but she started terribly against Muchova, much to the shock of the crowd.
Watched by her family, including her father, Terry, who owns the Buffalo Bills, Pegula sprayed errors around the court, with Muchova winning 19 of the final 23 points to rattle through the opener.
It looked as though the Czech, a beautifully deft player, would rout Pegula when she broke serve in the first game of the second set and backed it up for a 2-0 lead.
Pegula then found herself 30-40 down on serve and staring at a double break deficit, before Muchova missed a routine volley and momentum swung back towards the American.
Urged on by the crowd, the two traded breaks, before Muchova produced her worst tennis of the match to be broken and send proceedings to a decider.
Although Muchova upped her level, Pegula was dialled in, rarely missing from the baseline, and she claimed a crucial early break before advancing as her opponent speared a shot long.