The 27-year-old, who thanks to YouTube footage of his exploits for Norwegian club SK Brann was a terrace hero before he even arrived at Elland Road last month, opened the scoring with a vicious first-half drive and impressed all over the park as the Whites eased to victory.
Their second goal came from a wonderful close-range lob from teenager Sam Byram and their third from Tom Lees and, while Byram's goal will be remembered for longer, it was the performance of Austin that was the standout on the night.
A tough-tackling, free-shooting brute of a midfielder, he produced the best of his five performances for the club so far, breaking up play at will and bruising his way around the pitch as well as hitting the bar, as the League Two leaders found the step-up in class too much.
Quite whether Leeds' performance was worthy of being soundtracked by a string of 'oles' is questionable, but manager Neil Warnock will just be glad to see a side sporting six changes from his weekend one make it through without incident in front of a crowd that included Olympic medalist and United fan Jonny Brownlee.
As a result of the changes, and Oxford's early eagerness, the visitors started the better, with debutant goalkeeper Jamie Ashdown doing well to smother at James Constable's feet after Sean Rigg's shot had been charged down.
Leeds rode that period out, though, and after Austin had tried his luck from distance, they rarely looked back, with the same player's opener confirming that his side were on top.
Having scored from the halfway line on his final appearance for Brann, Austin is no stranger to the goal and displayed that in the 26th minute as he drilled Aidy White's pass into the bottom corner from 20 yards.
Goalkeeper Ryan Clarke actually did well to get a hand on it - something he could not do to Byram's effort nine minutes later.
The rookie full-back, fresh from signing a three-year deal, ran at Sean McGinty and once in the box, from 10 yards out, stood up a chip that left Clarke backpedalling and grasping at the air.
It was all Leeds now and El-Hadji Diouf drew a smart near-post save out of Clarke after being played in by Andy Gray, although Oxford did test Ashdown - for what turned out to be the only time - after the restart when Constable fired in from inside the box.
The 18-yard line was barely in sight for Austin in the 55th minute when he wound up a drive from fully 40 yards that thumped the bar, while Byram nearly scored a second when he volleyed just over after wonderful wing play from Diouf.
The Senegal international turned provider for Leeds' third with 16 minutes remaining too, floating in a ball that Lees headed in for his second of the season and it could have been more after that as White twice went close, but the home side had done enough.