The Clarets knew before kick-off that victory would see them bounce back into the top flight, having been outside the elite since their 2010 relegation.
And they were taking no chances, starting the game brightly with Barnes and Kightly handing the hosts a comfortable lead - the latter with his second goal in as many games.
Wigan improved after the break but the outcome was never in doubt and Burnley's fans were left to celebrate, invading the pitch, as their team guaranteed a top-two finish.
Trailing to Mathias Ranegie's goal six minutes into the second half, Rangers laboured before Joey Barton's 76th-minute free-kick hauled them level.
And top scorer Austin, badly missed during a recent two-month spell out with a shoulder injury, gloriously curled home his 16th goal of the season in the closing stages to clinch a 2-1 victory.
Rudy Gestede's hat-trick took the goalscoring spotlight away from Jordan Rhodes as Blackburn kept up their late push to reach the play-offs.
The former Cardiff frontman notched a first-half hat-trick with three smart headers in a 4-2 win at Birmingham, as Blackburn stretched their unbeaten run to 10 games.
It was humiliating for Birmingham who trailed Gary Bowyer's visiting side 4-0 at half-time and now find themselves in a desperate survival battle.
Matt Ritchie's deflected free-kick earned Bournemouth a 2-2 draw at Ipswich - a point that saw both clubs keep their top-six dreams alive.
Seventh-placed Ipswich twice led in front of their biggest crowd of the season at Portman Road thanks to goals from Paul Anderson and Paul Green, but they were pegged back, first by brilliance and then by good fortune.
Steve Cook's amazing overhead kick ensured parity at the interval and Ritchie made it a point apiece when his 20-yard free-kick was deflected off Cole Skuse and wrong-footed Dean Gerken.
Barnsley's chances of staying up were left hanging by a thread after a 2-1 defeat at play-off-bound Derby left them four points from safety with two games to play.
A glaring error by goalkeeper Luke Steele allowed Jeff Hendrick to put the Rams ahead before a deflected Johnny Russell shot increased their lead and, although Nick Proschwitz pulled a goal back, it came too late for the visitors.
Charlton inched towards safety after a Marvin Sordell hat-trick saw them recover from 2-0 down to win 3-2 at Sheffield Wednesday.
It represented a complete turnaround at Hillsborough, where Wednesday were two goals to the good after just eight minutes.
Doncaster overcame Abdoulaye Meite's first-half dismissal to secure what could prove to be a crucial point from a goalless draw with fellow strugglers Millwall.
Meite was given his marching orders following his mistimed challenge on Stefan Maierhofer, but Millwall could not make their numerical advantage count at The Den.
Brighton remain in the final play-off spot despite drawing 1-1 with Blackpool.
Dale Stephens had edged the hosts ahead with a fine effort from 20 yards but Stephen Dobbie struck just three minutes later to earn a point for relegation-threatened Blackpool.
Yeovil's survival bid was left in tatters after Huddersfield snatched a late 2-1 win at Huish Park.
Nahki Wells had put the Terriers ahead before Tom Lawrence grabbed an equaliser but Adam Clayton lashed in a late winner for the visitors to leave the Glovers six points from safety and rooted to the bottom of the table with two matches remaining.
- Sports & Recreation