Leeds eased the pressure on boss Thomas Christiansen with a rare victory at Barnsley in the Sky Bet Championship, running out comfortable 2-0 winners.
The Dane's position had come under scrutiny after a run of eight defeats from 10 games, including a 4-1 thumping at Wolves in midweek, and a visit to Oakwell, where United have won just once in 20 years, would not have been the most appealing prospect.
But they put in a performance for their boss and first-half goals from Saiz and Alioski wrapped up a convincing three points which puts them back on the tail of the play-off pack.
Barnsley, who had scored 17 goals in Leeds' last six visits down the M1, were not at the races and failed to register a shot on target until the 77th minute as their week ends with a second successive home loss.
That record at Oakwell might have had Leeds fearing the worst but there were no demons on show as it was the visitors that began with intent, with Alioski fizzing an effort just wide of the post after a loose ball had fallen to him 18 yards out.
A large melee upped the ante as Barnsley's Harvey Barnes squared up to Luke Ayling after accusing the right-back of diving and most of the pitch got involved in the ensuing scuffle.
Just eight minutes later Leeds were celebrating a deserved opener.
Saiz was given unlimited space in the Barnsley half and advanced unchallenged before unleashing an effort that went through the hands of goalkeeper Adam Davies, who might have expected to save it.
It was the Spaniard's ninth goal of the campaign.
Barnsley, for all their bluster, were carrying zero goal threat and their task looked insurmountable as Leeds doubled their lead in first-half stoppage time.
Some great pressing from Ayling won possession back and Alioski bent a fine curling effort into the bottom corner from the edge of the area.
Leeds might have expected some sort of backlash from their hosts after the break, but it was business as usual and Pablo Hernandez was inches from making it three when his free-kick was deflected just wide of the post.
Still the visitors looked more dangerous and Caleb Ekuban hit the side-netting after a lovely ball through by Hernandez while Liam Cooper's glancing header went straight to Davies.
Barnsley tried to up their levels and finally had a shot on target with 13 minutes to go, though Gary Gardner's effort will barely count as it trickled to Felix Wiedwald.
Leeds continued to look more likely with Alioski and Hernandez both firing over, but their first-half goals were enough to seal the derby spoils.