The striker, who had been one short of the three-figure milestone for almost a year, since netting in a 3-0 win over Crystal Palace at Selhurst Park, restored parity just minutes into the second half.
Deadline day signing Wout Weghorst was magnificent in the build up, taking two players out of the equation with a neat touch, before slipping a sublime reverse pass into his strike partner, who stepped across his marker before slotting the ball past David De Gea.
The Dutchman almost opened his account for the Clarets moments later when allowing the ball to drop before thumping it goal-wards from distance. However, De Gea got down impeccably to get a strong hand to the attempt as the ball arrowed towards the corner.
Those moments marked a significant shift from the home side's first half display as Ralf Rangnick's Red Devils blew them out of the water.
They had the ball in the net three times, though only one registered. That came from Paul Pogba in the 18th minute as the Frenchman passed the ball into the roof of the net from Luke Shaw's pull back.
Raphael Varane had guided a header past Nick Pope before hand, but the goal was chalked off following VAR's intervention after Harry Maguire was deemed to have obstructed Rodriguez as Bruno Fernandes' set-piece was delivered.
Josh Brownhill later inadvertently poked the ball into his own net from Marcus Rashford's pass, though Pogba had already been penalised for fouling Erik Pieters from Shaw's original delivery.
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