The visitors had enjoyed a 2-1 lead at the first intermission in the NIHL National encounter after goals from Alex Graham and Greg Wood, back out of retirement.
But three goals in as many minutes either side of the second break put Ben Morgan's team up against it, Harvey Stead getting the equaliser at 39.23 on the power play before further strikes early in the third from Dominik Gabaj - also on the power play - and Brendan Baird.
But a quickfire double from the visitors - Vladimir Luka's power play strike at 52.46 just 48 seconds ahead of Elliott's first strike of the night - put the teams level, leaving the Steeldogs' No 13 to seal his hero status two minutes into overtime.
Leeds Chiefs’ miserable run continued, with two weekend defeats extending their losing run to five games and leaving them seven points adrift of the playoff spots.
Injury and illness hit hard in Saturday’s 3-0 defeat at Telford Tigers, with four players missing from the line-up, although only import forward Andres Kopstals and defenceman Bobby Streetly remained out for Sunday night’s clash against Milton Keynes Lightning.
But even with defenceman Lewis Baldwin and top-scoring forward Adam Barnes back, Sam Zajac’s side were still outnumbered by their opponents.
It was two first-period goals from the returning pair that put the Chiefs ahead, although they found themselves hauled back by the end of the second period, the Lightning sealing the deal with two goals in the last five minutes.
Elsewhere, Hull Pirates went down 8-7 in a shootout against the Lightning the previous night, unable to build on that point when losing out 7-4 at home to Telford 24 hours later.
The teams were tied together at 2-2 at the end of the first after goals from imports David Norriss and Peter Fabus were traded with Telford's Brandon Whistle and Jason Silverthorn.
But it was the second period where the game got away from Jason Hewitt's team, with three Telford goals in five minutes giving the visitors an advantage - former Hull Stingrays favourite Silverthorn scoring twice to seal his hat-trick before Dominik Florian made it 5-2 at 27.28.
Fabus's second of the night made it 5-3 just over six minutes later, but Telford stretched their lead once more through Ross Kennedy at 37.32.
The first power play goal of the night went the way of the hosts when Lee Bonner struck at 48.12, but the league leaders had the final say with a strike on the man advantage themselves when Florian bagged his second with just 85 seconds remaining.