Gary Harkins ensured Ayr stayed in the contest when he reduced the deficit almost immediately after Austin’s second, but goals from Craig Sibbald and Fraser Aird at the death wrapped up a convincing win.
The Bairns have not been beaten this year and they seldom looked likely to surrender that proud record as they pushed Ayr deeper into a relegation dogfight.
United are now four points adrift of the safety of eighth place although they do have a game in hand over Raith Rovers.
Falkirk boss Peter Houston concedes catching Hibs will be difficult but perhaps not impossible.
He said: “Last night the gap was nine but it’s now back to six although they have a game in hand.
“We will take each game and hope that Hibs slip, I would much rather be in Hibs’ position than ours but we will keep battling away.
“Finshing second would mean two less games. Last year we were comprehensively beaten by Kilmarnock but we will learn from that. We will try and hang on to the coat tails of Hibs.”
Falkirk fans turned out in force and officials had to hurriedly open Somerset Park’s Railway End to accommodate a bigger than anticipated travelling support. And the Bairns fans were in full voice after only eight minutes when their team raced into the lead.
A quick break by Luke Leahy and John Baird ended with Austin having a strong shot beaten out by Greg Fleming.
When the loose ball spun free Austin was first to react to smash the ball high into the net.
Ayr were almost level when Craig Moore drove a fierce cross-cum-shot across the face of goal, Harkins only inches away at the back post.
Robbie Crawford tried to ignite Ayr as he darted past a couple of challenges into the box but the move ended with a Paddy Boyle shot which was blocked.
Ian McCall went for half-time surgery with Michael Rose replacing Brian Gilmour. And four minutes after the interval, Alan Forrest took the place of Moore.
However, Falkirk still looked far the likelier team and Austin showed great footwork in the box to send in a shot which was deflected past.
Austin looked to have put the game beyond doubt in 63 minutes, forcing the ball home at the second attempt after his initial header was smothered by Fleming.
But Ayr had an immediate riposte and within a minute pulled a goal back. Forrest’s darting run ended with a shot which Leahy scrambled off the line but Harkins followed up to smash the ball home.
Austin wasted a great chance for his hat-trick when he raced clear on goal but Fleming rushed off his line to block with Falkirk’s claims that he had been fouled falling on deaf ears.
Sub Lee Miller hit the post in the last minute but Sibbald broke clear to slide home a clinching third before Aird volleyed home a fourth in injury time to rub salt in Ayr’s wounds.
Ayr boss McCall felt the two late goals put a false complexion on the result.
He said: “I pushed Conrad Balatoni up front for the last five minutes and it backfired.
“The poor thing is we have lost Declan McDaid with an ankle injury and ended up playing with 10 men.”