A Karlan Grant strike just before half an hour had been played gave West Bromwich Albion the lead shortly before the half-hour mark, and as the game looked to be getting away from United, substitute Scarlett salvaged a draw.
Two minutes into stoppage time, Scarlett met a long throw-in with a header which flew past Alex Palmer in the Baggies goal.
Des Buckingham made two changes to the side which drew 1-1 at Portsmouth prior to the international break, as Elliott Moore returned to the heart of the defence in place of Sam Long, while Siriki Dembele came in for Kyle Edwards.
Before kick-off, there was a minute’s silence for two-time former U’s loanee George Baldock, who recently passed away aged just 31. Both teams wore black armbands during the game.
United had the first sniff of goal with seven minutes on the clock, as Mark Harris beat the offside trap, however his first touch took him a tad wide towards the left, allowing Palmer to make a save at his near post.
Will Vaulks hung the resulting corner to the back post and the ball fell to Elliott Moore, who stabbed an effort into the gloves of Palmer.
At the other end, Darnell Furlong drove into space and sent a strike wide from outside the penalty area.
A near post header from Torjbjorn Heggem flew narrowly off target from a corner, while Harris lined up a shot from 25 yards, but he sent it high and wide.
Albion took the lead just before half an hour had been played when calls for a foul on Dembele were waved away by referee Leigh Doughty seconds before Grant drilled a low strike into Jamie Cumming’s bottom right corner from 25 yards.
Ciaron Brown then headed just over from an outswinging Vaulks corner, before Uros Racic sent an effort off target when a Baggies corner fell to him 20 yards out from goal.
The final bit of action of the half saw Grant run infield from the left-hand side, before driving a right-footed strike into the midriff of Cumming.
The second period began with a slack ball across the Baggies backline almost presenting an opportunity to Dembele, who couldn’t quite get the ball out his feet to get a shot away.
Six minutes into the second half, Buckingham was shown a yellow card after Doughty blew for a free kick when Albion skipper Kyle Bartley hit the turf following a soft nudge in the back from Harris.
Dembele then went agonisingly close when he made his way to the byline, before cutting back to send in a cross which narrowly evaded both posts and skimmed out of play for a goal kick.
A loose ball fell to Racic centrally just inside the box and he fired a low strike through the bodies and into the gloves of Cumming.
Buckingham made a double switch with 64 minutes played, as Louie Sibley and Scarlett replaced Ruben Rodrigues and Harris respectively, and 10 minutes later, Malcolm Ebiowei came on for Dembele.
That change saw Crystal Palace loanee Ebiowei go to the right wing, with Tyler Goodrham moving over to the left.
The sting had been well and truly taken out of the fixture, and with seven minutes to go, Buckingham again looked to his bench to freshen things up.
This time, he sent on Owen Dale for Idris El Mizouni, as Dale lined up on the left, allowing Goodrham to drop back into midfield.
Five minutes of stoppage time were signalled, and two minutes into them, Scarlett headed United level.
A long throw from Vaulks was hurled into the penalty box, and Tottenham Hotspur loanee Scarlett rose well to head home after Moore had initially flicked the ball on.
Oxford United (4-3-3): Cumming; Kioso, Moore, Nelson, Brown; Rodrigues (Sibley 64), Vaulks, El Mizouni (Dale 83); Goodrham, Harris (Scarlett 64), Dembele (Ebiowei 74).
Unused subs: Ingram, Long, ter Avest, Leigh, Goodwin.
Booked: Nelson, Sibley.
West Bromwich Albion (4-2-3-1): Palmer; Furlong, Ajayi, Bartley, Heggem; Racic (Molumby 83), Mowatt; Fellows (Wallace 70), Diangana (Swift 70), Grant; Maja (Johnston 83).
Unused subs: Wildsmith, Styles, Diakite, Dobbin, McNair.
Booked: Mowatt.
Referee: Leigh Doughty (Lancashire)
Attendance: 11,453 (TBC visitors)