Coaches Mike Stowell and Chris Powell took charge as Eriksson watched from the stands at the Walkers Stadium, with a two-year deal waiting to be signed by the Swede.
The 62-year-old is expected to succeed Paulo Sousa as boss and he witnessed a performance that belied their position in the doldrums of the Championship.
City bossed the first-half and Martyn Waghorn gave them a deserved early lead as Scunthorpe laboured, leaving their rookie chief Ian Baraclough still searching for his first win in full charge.
Lloyd Dyer doubled the lead and not even Michael O'Connor's response on the hour could derail the Midlanders from victory as Franck Moussa notched a late third.
Leicester's temporary management pair made three changes from the team that lost 4-3 in midweek to Norwich, with Miguel Vitor and Bruno Berner coming into the defence. Paul Gallagher came into midfield while warhorse striker Steve Howard was named captain.
Bobby Grant made his full debut for Scunthorpe as Rob Jones' broken hand meant he made way for Niall Canavan.
All eyes were trained on the directors' box prior to kick-off for a sight of former England chief Eriksson, and he will have been impressed by his potential new charges.
The snappers may have missed the first chance of the match as Andy King went within a whisker of handing Leicester a first-minute lead as he headed over from Gallagher's centre.
City didn't have to wait long to make the breakthrough as Waghorn exchanged passes with Gallagher on the edge of the area before producing a smart finish past Joe Murphy in the 10th minute.
Sousa's undoing had undoubtedly been a poor defensive record which saw his team concede 22 times in nine outings and their caretaker duo ensured the Foxes' rearguard tightened up.
It meant United struggled in the final third and Jonathan Forte - making his 100th league start - had a sniff of an opening but his timid shot did not trouble Carl Ikeme.
At the other end Murphy was called into action as he beat away Lloyd Dyer's drive but skipper Howard spurned the chance for a second from the resultant corner, heading over from seven yards.
More shaky Scunthorpe defending nearly saw David Mirfin put past his own keeper in a mix-up with Murphy but the Iron escaped to the interval just a goal behind.
But their jitters continued after the restart as Leicester extended their lead as Dyer lashed home in the 54th minute, and even though substitute O'Connor pulled one back after Eddie Nolan's shot came back off the post, they held firm for all three points to move away from the bottom of the division thanks to Moussa's goal in stoppage time.