After a first half that was only notable for the weather conditions, the game sprang into life in the final half hour.
There had been little between the two sides until substitute Chris Wood scored four minutes after his introduction, the Kiwi tapping home a centre from Hadi Sacko from close-range.
But like Saturday, Rovers responded quickly, Marvin Emnes blasting his first goal for the club in emphatic fashion with 13 minutes remaining.
The Lancashire side pressed for a winner with Robert Green denying Emnes and Sam Gallagher in quick succession. They would prove to be pivotal saves as Leeds claimed all three points mere seconds later when Kyle Bartley headed in Alex Mowatt's free-kick to leave Rovers at the bottom of the table.
Before the game Owen Coyle made just the one change from the side that drew with Queens Park Rangers on Saturday.
With Charlie Mulgrew sidelined with a calf strain, his place in midfield, like at Loftus Road, was taken by Corry Evans.
The hosts made three changes following their weekend loss at the hands of Huddersfield. Eunan O'Kane, Stuart Dallas and Pablo Hernandez coming in for Chris Wood, Kalvin Phillips and Alex Mowatt.
Rovers scored after 17 seconds on their previous visit to Elland Road, but the only early drama on this occasion was when Robert Green fouled Sam Gallagher outside his area after six minutes.
The Rovers striker beat the Leeds keeper to the ball before being clattered to the ground. The former England man perhaps fortunate to be only shown a yellow card by referee James Adcock.
That lead to a five minute break as both players received treatment to head injuries. When play eventually resumed Ben Marshall's free-kick came out to Craig Conway who struck well on the half-volley but over the bar.
O'Kane saw an effort clear the crossbar from distance, before Derrick Williams made an important tackle to thwart Hadi Sacko in front of goal.
But as the weather worsened, with heavy rain and repeated bursts of thunder and lightning, there was little in the way of goalmouth opportunities from either side as the half ended goalless.
Both sides looked to make an early impression as the teams returned at the start of the second half.
Marshall was the first to try his luck from distance, his 20-yard daisy-cutter flashing just past the post.
Sacko then saw a shot deflect over his own bar by Tommie Hoban, before Stuart Dallas had a near post effort claimed by Steele.
Hope Akpan was next with an effort at goal but his dipping half-volley didn't trouble Rob Green's goal.
But as the half wore on it was the Whites who were slowly building up a head of steam with Rovers unable to get any meaningful possession.
A Hernandez corner picked out Kyle Bartley, but his header bounced up and over the bar.
Both sides made striking changes with Marvin Emnes on for Danny Graham, whilst Chris Wood replaced Marcus Antonsson. And it was New Zealander Wood who would put the home side in front on 65 minutes.
Sacko had shown a quick turn of pace all evening and as he raced into the area, he's pass across the six-yard box was tapped home by Wood.
Rovers lost Tommie Hoban through injury, but the visitors brushed off that disappointment by grabbing a sensational equaliser 13 minutes from time.
There seemed little on as Emnes picked the ball up 20-yards out, but the Dutch forward smashed an unstoppable drive into the back of the net for his first Rovers goal.
Suddenly it was all Rovers, Emnes couldn't connect in front of goal after Gallagher had nodded on Jason Lowe's centre, then Green made two vital saves to keep the visitors at bay.
Emnes went searching his second of the game when he collected a pass from Marshall, but Green saved with his chest, Gallagher showed great acrobatics to try and hook home the rebound, but the Leeds keeper pulled off an unbelievable reaction save.
They would prove to be pivotal as Leeds went up the other end to score the goal that would see them claim a first home win of the season.
After sub Darragh Lenihan was adjudged to have fouled Sacko on the far side. Alex Mowatt delivered the free-kick into the box to where Bartley rose highest to head home.
Rovers were given hope when seven additional minutes were shown, and although they delivered ball after ball into the Leeds box, the home side held on to claim the victory and leave Owen Coyles men still searching for theirs.
LEEDS: Green, Ayling, Bartley, Antonsson (sub Wood 61 mins), O'Kane (sub Mowatt 83 mins), Dallas, Jansson, Hernandez, Taylor, Sacko, Bridcutt (sub Phillips 49 mins).
Subs not used: Silvestri (GK), Cooper, Doukara, Coyle.
Goals: Wood 65 mins, Bartley 87 mins.
Booked: Green 6 mins, Sacko 44 mins, Ayling 79 mins.
ROVERS: Steele, Lowe (c), Greer, Hoban (sub Lenihan 75 mins), Williams, Evans, Conway, Akpan (sub Feeney 71 mins), Marshall, Gallagher, Graham (sub Emnes 61 mins).
Subs not used: Raya (GK), Byrne, Samuelsen, Guthrie.
Goals: Emnes 77 mins.
Booked: Greer 26 mins, Evans 81 mins, Marshall 90+8 mins.
Attendance: 19,009 (including 327 Rovers fans)