Logan's mistake just after the hour mark swung Tuesday night's fourth-round tie at the Walkers Stadium firmly in the visitors' direction.
The Foxes number 13 was under no pressure when he went to collect Gianni Zuiverloon's over-hit long ball but, having seemingly caught it, he failed to hold on and presented Somen Tchoyi with the simplest of finishes reminiscent of his recent strike at Old Trafford courtesy of Edwin van der Sar's mistake.
The goal put Albion back in command at a crucial period in the tie when Nicky Shorey's own goal had cancelled out Simon Cox's composed finish from the first half to level things up. Steven Reid ended the tie as a contest 11 minutes from time before Cox grabbed a stunning second to book the Baggies' place in the last eight for the first time in seven years. Despite their exit, the result
at least leaves Foxes boss Sven-Goran Eriksson to focus on the club's number one ambition this season - promotion to the Premier League.
West Brom counterpart Roberto Di Matteo changed his entire XI from Saturday's 2-1 win over Fulham.
Reid was handed the captain's armband upon his return, with the likes of Cox, Roman Bednar, Graham Dorrans and Giles Barnes coming back in.
Ishmael Miller, a loan target for Eriksson, was named on the bench on his comeback from injury.
Eriksson himself changed eight players from the weekend's 2-0 defeat at Swansea - his first loss as Leicester boss - with a handful of loan players cup-tied.
Albion fans took obvious delight at the arrival of former striker and boyhood Baggies fan Lee Hughes in the visiting stand they occupied.
And he would have watched a pretty ordinary opening quarter littered with mis-placed passes and the surrender of possession as 19 incoming players looked to get a feel of the game. Foxes midfielder Paul Gallagher enjoyed the first effort of the encounter in the 13th minute and was not too far away with his low drive from 25 yards.
The hosts were providing the greater attacking threat early on but it was Albion who broke the deadlock with their first real attack in the 21st minute.
Left winger Barnes beat Bruno Berner for the first time and crossed to the back post where Tchoyi found Bednar, who in turn saw his shot deflected into the path of Cox, who produced an exquisite dink over Logan.
Lloyd Dyer and Gallagher were looking the most threatening players for the Championship side and it was the latter who almost levelled matters with a free-kick which had Boaz Myhill scrambling across his goal.
Baggies midfielder Tchoyi then curled an effort wide before Logan saved Leicester from going two down shortly before the interval when his outstretched arm tipped Bednar's looping header wide.
West Brom could and should have been two goals to the good within minutes of the restart and Tchoyi's inch-perfect throughball deserved better from Dorrans who seemed to get caught in two minds and aimed a weak, bobbling shot come cross towards the far post.
The top-flight outfit were made to pay with 53 minutes on the clock when, amid a spell of home pressure, the ball was recycled to Gallagher in acres of space on the right and his cross was deflected into his own net by half-time substitute Shorey at the near post.
Chances came at either end before Albion regained the lead in the most fortuitous of circumstances just after the hour mark.
Zuiverloon's long ball from right-back looked to be a simple catch for keeper Logan but he made the biggest of clangers to present Tchoyi with the simplest of finishes.
Logan went some way to redeeming himself with an impressive save from Shorey's free-kick and Barnes' low shot.
But Reid wrapped the game up as a contest in the 79th minute when he rose unmarked at the far post to head Barnes' corner into the roof of the net.
And it was left for Cox to round off the scoring with a superb long-range strike into the top corner which left Logan with no chance in the final minute.