United defender Maguire, who was celebrating a return from the international wilderness, was dismissed for a foul on Evanilson, allowing Cherries substitute Junior Kroupi to equalise with an 81st-minute penalty.
The visitors were twice on course to move within four points of second-placed Manchester City after Bruno Fernandes opened the scoring from the spot and a James Hill own goal restored the advantage following Ryan Christie's initial leveller.
But United will instead be looking over their shoulders at the chasing pack of Aston Villa, Liverpool and Chelsea after dropping points for only the third time in 10 top-flight fixtures under head coach Michael Carrick.
In an action-packed second half, the away side felt aggrieved not to be awarded a second penalty following a potential foul by Adrien Truffert on Amad Diallo, immediately before Christie equalised.
United's resurgence since Carrick replaced Ruben Amorim in January was underlined on Friday by Maguire and Kobbie Mainoo returning to the England set-up for the first time since September 2024.
The pair started in an unchanged team after Sunday's 3-1 success over top-four rivals Villa, while Bournemouth recalled Alex Jimenez and Amine Adli in place of Adam Smith and Kroupi.
Diallo stung the palms of diving Cherries goalkeeper Djordje Petrovic inside five minutes before Rayan dragged wide at the other end moments later following a counter-attack led by Marcus Tavernier.
After Matheus Cunha tested Petrovic, Rayan forced a stop out of United goalkeeper Senne Lammens and Tavernier turned narrowly wide, before Diallo's powerful volley was blocked by Truffert.
Diallo fared slightly better eight minutes later as United almost edged ahead. The full-back's cross from the right was thumped goalwards by Fernandes at the back post, only for Petrovic to save with his left leg.
In the second half, Cunha went down theatrically in the box following a shirt pull from Jimenez and Fernandes calmly rolled the ball into the bottom-left corner.
United wanted another spot-kick when Diallo went to ground under a challenge from Truffert before Christie launched a counter-attack which culminated in him sweeping the ball into the bottom-right corner from just inside the 18-yard area.
Four minutes later, Fernandes' inswinging corner from the left was flicked on by the head of Cherries defender Marcos Senesi and inadvertently diverted home by his centre-back partner Hill, under pressure from Maguire.
Bournemouth midfielder Alex Scott rattled the frame of the goal from distance before his side claimed a point with nine minutes remaining.
Referee Stuart Attwell produced a straight red card after Maguire impeded Cherries striker Evanilson as he burst into the box, and Kroupi emphatically thumped the resulting penalty into the bottom-left corner.
