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.
Here are the ratings.
1. Nick Pope 7.5
Beaten three times, but only one counted. Much busier in the first half than he was after the break; a sprawling save to his left hand post to deny Cavani a tap-in was the pick of the bunch. Also denied Rashford twice, getting his legs in the way to block well in the second instance. Photo: Catherine Ivill
2. Connor Roberts 6
Became too tied up with Sancho and Shaw to be able to roll the dice and get forward in support of McNeil, particularly in the first half. Will be disappointed not to have applied more pressure to United's overlapping full back to prevent his assist. However, came to the party after the break. Photo: George Wood
3. Erik Pieters 6
Deputised for Taylor against City, Arsenal and Manchester United now. Struggled to shut up shop in the first half as Rashford threatened, but won a number of crucial flicks from raking cross-field passes, covered almost the full length of the pitch when embarking on a first half counter while a fizzing volley whistled past the post. Photo: James Gill
4. James Tarkowski 7.5
Rock solid at the heart of the Burnley defence. Beaten by Varane when the Frenchman's goal was ruled out, but rarely put a foot wrong otherwise. Cavani's anonymity spoke volumes of his performance and he made some timely second half challenges to keep United at bay. Photo: Nathan Stirk