The Ryman Premier League side were the lowest ranked team left in the competition but put up an incredible fight against their Premiership opponents.
They kept the Magpies out until half-time and never looked out of their depth even after Lee Bowyer and Shola Ameobi sealed victory for the visitors early in the second half.
Spurred on by Exeter's exploits at Old Trafford 24 hours earlier, Yeading made an astonishing start to the match.
They played totally without fear in the first half, attacking Newcastle at every opportunity and showing drive and skill in midfield.
There was an exciting, free-flowing feel to Yeading's football, unfettered by nerves or pressure.
Captain David Clarke, Darti Brown and Davis Haule in particular were outstanding in midfield, taking every opportunity to attack.
Their best chance to open the scoring came after 23 minutes when Clarke saw a 20-yard free-kick superbly turned around the post by keeper Steven Harper.
Defender Emond Protain also sent a header narrowly over the bar from an excellent Alex Stanley free-kick.
But, bad as Newcastle were, the visitors did create a string of chances of their own.
They may have been out-enthused in most areas of the pitch, but they reached half-time wondering how on earth they had not scored.
The first culprit to miss a sitter was Laurent Robert, who found himself free on goal after one minute, but hit his shot tamely at Ding keeper Delroy Preddie.
Bowyer then produced an even worse miss from close range, while Shola Ameobi had one shot saved and fired another well over the bar.
On top of that Bellamy hit the bar after 19 minutes and Jermaine Jenas saw a superb 25-yarder well saved.
But Yeading got to the break on level terms and the dream was only ended by a much-improved Newcastle in the second half.
First, Bellamy raced down the right after good work by Ameobi and sent over a low cross for Bowyer to easily tap home in the 51st minute.
Then, ten minutes later, Ameobi superbly headed home a free-kick from substitute Darren Ambrose.
Many thought Yeading would collapse, but in fact they held their own and did non-league football proud.
And they almost ended the match on a high when Brown's superb 25-yard drive was spectacularly turned around the post by Harper.