Anthony Gordon's first goal for the club since his January move from Everton gave the Magpies the lead at Stamford Bridge, but Kieran Trippier's unfortunate own goal evened things up before the break.
And that's the way it stayed in London, with United head coach Eddie Howe's side ending the season in fourth place - and they could even have signed off with a victory, had teenage debutant Lewis Miley's effort dipped in instead of clipping the crossbar late on.
Howe rung the changes for the trip to the capital, with Martin Dúbravka, Matt Targett, Allan Saint-Maximin and Gordon all coming into the United side as they looked to bring the curtain down on a terrific campaign in style.
And less than ten minutes in, they were able to take a step towards doing just that when former Everton winger Gordon tapped in his first goal in black and white. The goal owed much to good work from Saint-Maximin and Elliot Anderson down the left, with the youngster's low cross perfectly weighted for Gordon to attack and prod past Kepa Arrizabalaga to give the visitors the lead.
It was a lively opening to the contest and just before the half hour, Chelsea pulled level. Raheem Sterling cut inside from the right after a quickly-taken free kick and his shot was low, but Trippier's attempted clearance went wrong, with the ball bouncing up onto his arm and into the net to hand the Blues an equaliser.
Miguel Almirón pulled a shot wide of the target soon after and then miscued when presented with another opportunity soon after as Newcastle looked the likeliest team to move back in front, but the Paraguayan, typically, kept going. Another attempt was stopped by Kepa but the hosts went even closer before the break, as Dúbravka pulled off an eyecatching save to deny Sterling and Targett nodded the follow-up off the line.
The second half's early exchanges were slightly cagier, with both sides probing for chances in the final third. Manchester United's second goal in their eventual 2-1 victory over Fulham meant the Magpies' hopes of finishing third were dashed and in truth it was Lampard's charges who had the better of proceeding in the final 45 minutes of the campaign, with both Sterling and Lewis Hall having fleeting sights of goal.
England wideman Sterling blazed over with his unfavoured left foot in another attacking burst as the contest drifted towards its conclusion, with Howe electing to send on Jacob Murphy and Callum Wilson for the final 20 minutes.
But the most noteworthy of all the afternoon's substitutions was another of Howe's, as the United boss handed a senior debut to teenage midfielder Miley at the age of 17. He came on to a rapturous reception from the travelling supporters and though Sterling squandered another fine opening seconds later and both Christian Pulisic and Joao Felix could both have won it at the end, the day almost belonged to the Newcastle debutant, whose promise was clear in his cameo. Miley's strike, which hit the woodwork, would have provided a fitting finish to what has been a magnificent nine months for those in black and white.
