A dramatic 99th-minute winner from Alex Iwobi gave 10-man Newcastle a 1-0 win after Allan was controversially sent off.
The home side found chances difficult to come by and could only get one shot on target, seeing just over 40% of possession.
After both sides spent heavily with new managers in the January transfer window in an attempt to secure Premier League survival for at least one more season, it was Newcastle who were more impressive, but they too could not break down the opposition.
Eddie Howe has recently refused to be drawn on the political implications of managing Newcastle United, and Lampard has been similarly reticent to discuss Chelsea and Manchester City having played for them both, but there was one political intervention neither of them could avoid.
In the second half, a spectator used a plastic zip tie to connect himself to a goalpost while wearing ‘Just Stop Oil’ emblazoned on his t-shirt. The game was paused until he was removed.
However there was late controversy as Everton were denied a penalty as Seamus Coleman appealed, and on 83 minutes Allan was sent off for a lunge after a VAR review, with his challenge on Allan Saint-Maximin ruled to be sufficiently dangerous to warrant a red.
Then, on 99 minutes Iwobi popped up to grab all three points for Everton.
The point sees Newcastle on 31 points in 14th, and likely safe. Everton though remain in 17th, now three points clear of Watford, and with two games in hand on the Hornets.