Sven-Goran Eriksson took charge at the start of October with the Foxes in the bottom three but Monday's Walkers Stadium victory was the clearest indication that, with money to spend this month, they will have a strong say in the promotion shake-up.
Recalled left-back Bruno Berner opened the scoring in the sixth minute with his first of the season, although the lead did not last long as Scott Sinclair's stunner - his first goal in nine games - levelled matters.
The hosts had failed to score from a corner all season going into Monday's game but their 43rd-minute winner was almost a carbon copy of the first from Paul Gallagher's set-piece, Vassell appearing to get the final touch with Andy King in close proximity.
The winner rounded off a thoroughly-entertaining first half played between two footballing sides at a high tempo, although the second failed to live up to the same billing.
Nevertheless, victory leaves Leicester still unbeaten at the Walkers Stadium in the league since Eriksson took the reins.
The hosts, who failed to get international clearance in time for new boy Sol Bamba to feature but did include loan signing Ben Mee on the bench, made a rapid start to proceedings and had already twice gone close prior to Berner's early opener.
Gallagher saw his 15-yard volley deflected wide by Swans skipper Garry Monk, with the resulting corner also going close as it was again sent behind for another Foxes set-piece.
And it was from that which Berner struck, following up to convert from close range after his initial header had been parried by Dorus de Vries.
Yet the lead lasted all of six minutes as Sinclair levelled with a memorable strike.
Neat approach play involving Angel Rangel, Darren Pratley and Sinclair led to the latter curling a delightful right-footed effort inside the far post from over 20 yards.
The goal visibly gave Swansea confidence after a shaky start as they grabbed a foothold, but it really was end-to-end stuff with Leicester giving as good as they got, despite not many clear-cut openings being created.
And with the direction of the next goal anyone's guess, it was the Foxes who edged back in front two minutes before the interval via an almost replica of their first.
De Vries could only parry Jack Hobbs' header from Gallagher's corner and Vassell was on hand to convert, with King lurking closely.
King could well have got his goal within two minutes of the restart, glancing Gallagher's free-kick narrowly wide.
And it was Leicester who held the upper hand over a large part of the second half although the overall tempo of the game had certainly slowed from the opening 45 minutes.
De Vries made a great stop to deny Vassell with 69 minutes gone.
And Swansea's chance to snatch a point came with 12 minutes remaining but Sinclair could only fire wide when well placed, extending the visitors' 61-year wait for victory on Leicester soil.