Erik ten Hag’s side appeared on course to establish an eight-point cushion in fourth place as clinically-taken first-half goals from Jadon Sancho (7) and Marcus Rashford (44) put them in control.
But Spurs pulled one back through Pedro Porro (56) then forced a deserved equaliser when Son converted Harry Kane’s low cross (79).
The draw takes Spurs up to fifth, six points behind United having played two games more, and ensures United still have work to do to be sure of Champions League qualification.