Raducanu has not secured a win over a top-10 player since beating Emma Navarro in March, losing eight matches in a row against elite opposition, but she appeared determined to stop the rot.
But a series of delicious Pegula forehands saw the fifth seed break back and pile the pressure on Raducanu while down 4-3.
However, moments later, Raducanu secured her second break of the first set. She took advantage when Pegula mis-hit a drop-shot at the net and the 22-year-old then blasted an angled forehand across court to put herself on the verge of a huge advantage.
Raducanu sealed a gripping first set 6-3 with her mum, Renee, cheering on from the sidelines as she made a rare appearance to watch her daughter play in person.
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Pegula had lost 10 of her last 14 first sets and is well-equipped and making comebacks, but Raducanu maintained her form with two stunning forehands in the third game, en route to another early break.
The recent US Open semi-finalist proved to be no pushover and immediately broke right back from 30-0 down and the momentum appeared to swing in her favour before a gutsy hold of serve.
She won six points in a row, but in a match that featured plenty of twists and turns, Raducanu fought back to hold at 4-4.
Renee was on her feet as Emma pulled off a stunning backhand at 5-5, though she was unable to break the American, who closed the game with a stunning backhand winner down the line. Raducanu did hold comfortably, though, sending the second set to a tiebreak thanks to a pair of aces.
They traded mini-breaks in a scintillating tiebreak and both players produced strong groundstrokes against perfect defending, but the Brit could not get over the line despite having three match points.
Raducanu’s energy appeared sapped, similarly to her recent defeat to Barbora Krejcikova, and Pegula raced into a 3-0 lead in the deciding set through two immediate breaks of serve.
The lead quickly stretched with another hold, and break, with Pegula finally serving out to clinch a 6-0 set win, bagelling Raducanu to secure a place in the fourth round.
She will face 23rd seed Maria Kostyuk in the last 16, paving the way for a potential quarter-final showdown with reigning Wimbledon champion Iga Swiatek.
