But humble Cambridge were undaunted as Joe Ironside fired in a second-half goal and keeper Dimitar Mitov made a series of saves to deliver a fairytale win their 5,000 visiting fans celebrated in ecstatic fashion.
Bulgarian keeper Mitov made an incredible save in stoppage time to deny Joelinton an equaliser and Eddie Howe's side were booed at the final whistle as Newcastle's season went from bad to worse.
"I have got to play here and it is stuff I dreamed of. Alan Shearer was my hero, I grew up idolising him -- now I have scored the winner at St James' Park," Ironside said.
"It's a momentous day for the club."
Leicester, who stunned Chelsea in last season's final to win the competition for the first time, welcomed back former title-winning manager Claudio Ranieri but showed him no sympathy in a dominant display interrupted only by a floodlight failure.
Youri Tielemans put them ahead from the penalty spot and James Maddison made it 2-0. Joao Pedro replied for Watford but second-half goals by Harvey Barnes and Marc Albrighton sealed Leicester's place in the fourth round draw.
Chelsea were clinical against Chesterfield with Timo Werner, Callum Hudson-Odoi, Lukaku and Andreas Christensen all on target in a predictably one-sided first half.
Hakim Ziyech made it 5-0 but Chesterfield's Akwasi Asante sent the thousands of visiting fans wild with a consolation goal.
Burnley became the first Premier League casualty of the third round when they lost 2-1 to Huddersfield Town for whom Matty Pearson headed a late winner.
Everton's under-pressure manager Rafa Benitez earned a little respite as his side edged out Hull City 3-2 having fallen behind in the opening minute -- Andos Townsend securing only his side's second win in 13 matches in extra time.
Crystal Palace came from a goal to down to win 2-1 against London rivals Millwall with goals from Michael Olise and Jean-Philippe Mateta while Brentford enjoyed a comfortable 4-1 victory away to Port Vale thanks to a Bryan Mbeumo hat-trick.
Brighton & Hove Albion beat Championship promotion chasers West Bromwich Albion 2-1 after extra time at the Hawthorns.
Ten-man Southampton edged a 3-2 victory after extra time at second-tier Swansea City -- a game played in an empty stadium because of Covid-19 restrictions in Wales.
Shane Long scored the winner for Saints who played 90 minutes with a man less after Yan Valery was red-carded.
Minor league Kidderminster Harriers, the lowest-ranked team in the third round, caused a shock when the sixth-tier club beat Championship side Reading 2-1.
"I'm stuck for words," said manager Russ Penn after his side bridged a 79-place gap on the English soccer ladder. "I'm so proud of the players and the football club."
Boreham Wood made it two non-league sides in Sunday's fourth round as they beat AFC Wimbledon 2-0.
Cambridge, 16th in League One, swept away the new year optimism at Newcastle, for whom Trippier's signing is likely to be just the first in January for the club bought by Saudi Arabia's Public Investment Fund in October.
They rode their luck at times and had Mitov to thank for several saves, one an amazing fingertip effort to deny Jacob Murphy, while Newcastle's Fabian Schar had a goal ruled out.
But Cambridge were always a threat and Ironside fired in from close range in the 56th minute and it proved enough to provide the day's big shock.
"I don't think there was anything wrong with our attitude, we just couldn't deliver the quality to score," Howe said.