Jagielka turned the ball past his own goalkeeper Aaron Ramsdale early in the second half after Ben Osborn had cancelled out Jack Harrison’s early opener for Leeds.
The Blades, cast adrift at the foot of the table, battled gamely throughout and were not without their chances.
But Leeds created plenty more as they passed the 40-point mark with their 13th league win of their first season back in the Premier League, which lifted them back into the top half of the table.
Kalvin Phillips and Stuart Dallas both forced Ramsdale into full-stretch saves as Leeds went straight on to the offensive.
- Liverpool’s rematch with Real Madrid is about more than revenge
- England Euro 2020 squad: Who’s on the bus, who could miss out?
- British basketball has done so much with so little but its potential has never been greater
- England players must realise their power after passing up chance to protest over Qatar
But Ramsdale was helpless when Raphinha’s ball in across the face of goal to the far post picked out Harrison, who tapped Leeds into a deserved 12th-minute lead.
David McGoldrick curled a right-footed shot wide for the Blades, who were almost caught out on the counter after enjoying a rare spell of possession. Patrick Bamford broke down the right and after the ball was deflected into the area following George Baldock’s challenge on Tyler Roberts, Harrison’s attempted low finish was deflected wide by Ramsdale.
Baldock required treatment after banging his head on the turf - he was fortunate not to have been cautioned for leading with his feet - and he was later replaced by Ethan Ampadu.
Roberts unleashed a powerful low drive just off target and when it seemed Leeds would have to settle for a 1-0 lead at the interval, the visitors struck in first-half stoppage time.
Raphinha carelessly gave the ball away in midfield and although Oliver McBurnie’s shot was charged down, the ball fell to Osborn and his effort had clearly crossed the goal-line when it was blocked by Luke Ayling.
Leeds were soon back in front, regaining the lead four minutes after the restart.
Roberts’ diagonal ball found Harrison and as his attempted low cross aimed for Raphinha at the back post was diverted past Ramsdale by the sliding Jagielka. It was the former England defender’s seventh Premier League own goal.
Dallas’ shot soon after clipped the crossbar and Gjanni Alioski fired wide as Leeds took full control again.
Jayden Bogle then threatened for the visitors as his effort was deflected for a corner and at the other end Dallas pulled his low shot narrowly wide following a sweeping move instigated by Raphinha.
Rhian Brewster crashed a 25-yard effort just wide and fellow Blades substitute Oliver Burke’s low effort was just off target as the visitors chased an equaliser, but Leeds continued to look menacing on the break.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies