Roberto Di Matteo's buoyant Albion extended their impressive run of form to eight matches without defeat when two goals from Simon Cox, supplemented by Somen Tchoyi and Steven Reid, secured a place in the last eight of the Carling Cup for what was effectively their reserve team.
Leicester had recovered from a first-half deficit to equalise early in the second period before the contest turned on a moment of misfortune for their goalkeeper Conrad Logan, whose howler allowed Albion to regain the lead and deflated Sven Goran Eriksson's Leicester.
The 24-year-old Irish goalkeeper, who let in six goals in his last appearance this season, spilled a routine take from a long ball into his penalty area, allowing Tchoyi to tap the ball in.
It was the second time this month the Cameroon international had benefited from a keeper's mistake, having cashed in on Edwin van der Sar's blunder to score the equaliser in Albion's 2-2 draw in the league at Old Trafford.
Di Matteo may be a rookie among top-flight managers but he has clearly read the page in the manual headed "What To Do About the Carling Cup". He put out an entirely different team from the one that beat Fulham to go fourth, if only for a few hours, in the Premier League on Saturday.
Having beaten Manchester City last time out, the 10 survivors from that match probably felt they deserved to keep their places. They seemed to have a point, too, when they took the lead after 21 minutes, when a deep cross by Giles Barnes was played back in by Tchoyi before Roman Bednar took a swing and the ball ultimately reached Cox, who deftly chipped Logan from close range.
Eriksson, who already knew the Carling Cup etiquette, had made eight changes of his own from the side beaten at Swansea at the weekend. Ironically, winning three Carling Cup ties was about the only thing his hurriedly dismissed predecessor, Paulo Sousa, was seen to have done right in his brief period in charge, but for Eriksson, climbing away from the lower reaches of the Championship is of greater concern.
The home side had pressed without troubling Boaz Myhill as often as they would have liked in the first half but drew level after 53 minutes when Paul Gallagher's shot beat the keeper with the aid of a deflection off Nicky Shorey, the Albion left-back. Although the winger's strike might not have gone in unaided it was a poor goal from Albion's viewpoint, set up when Franck Moussa dispossessed Graham Dorrans and found Gallagher unmarked on the right.
If that was an uncomfortable moment for Myhill, however, it was nothing next to the embarrassment suffered by Logan when Gianni Zuiverloon's long ball slipped through his hands with such disastrous consequences.
Logan redeemed himself in part when he tipped a Shorey free-kick over the bar but was beaten again from the ensuing corner, nodded in by Reid to secure Albion's win with 11 minutes left, before Cox hit his second of the night from long range in the closing moments.
Unusually, anger showed through Eriksson's polite demeanour afterwards. "The score makes it look like a cruise for West Brom and it wasn't," he said. "We played rather well but if we continue to defend like that we will get nowhere.
"You cannot blame the goalkeeper. He will not sleep tonight but for me the third and fourth goals were worse."
Leicester City (4-3-3): Logan; Neilson (Lamey, 70), Morrison, Vitor, Berner; Abe, King (Fryatt, 67), Moussa; Dyer (Wellens, 54), Howard, Gallagher. Substitutes not used Weale (gk), Teixeira, Kennedy, Hobbs.
West Bromwich Albion (4-2-1-3): Myhill; Zuiverloon, Meite (Mantom, 79), Ibañez, Cech (Shorey, h-t); Dorrans, Reid; Cox; Barnes, Bednar (Miller, 85), Tchoyi. Substitutes not used Carson (gk), Mattock, Jara, Tamas.
Referee A Taylor (Manchester).