The hosts were the better side for large spells of the contest but it was Cambiasso's unfortunate touch off Wes Morgan's header in the 47th minute that ensured West Brom took home the bragging rights.
The Baggies have now lost only once in six league matches while Leicester have picked up just one point from five fixtures that included Swansea, Newcastle, Burnley and Crystal Palace.
A disappointing performance last weekend prompted Nigel Pearson to make four changes to the Leicester line-up as leading scorer Leonardo Ulloa, without a goal or a shot in his last four matches, was dropped to the bench.
Marcin Wasilewski was among those to come in and he tested Ben Foster with an early header from Matty James' corner before the West Brom keeper almost got himself into trouble when he carried the ball suspiciously close to the edge of the penalty area.
Saido Berahino looked dangerous with his pacey runs in behind Leicester's defence and with quarter of an hour gone, the in-form striker finally beat the hosts' offside trap but his shot was held by Kasper Schmeichel.
At the other end, referee Stuart Attwell turned down two penalty appeals in quick succession as Craig Dawson met a Leicester free-kick with the top of his arm before Joleon Lescott cleared out both man and ball after Jamie Vardy had latched onto Craig Gardner's sloppy back-pass.
It was from set-pieces that the home side looked most likely to break the deadlock.
Morgan flashed a header wide from another James corner and moments later City's captain was involved again as the ball dropped to Danny Drinkwater eight yards out but the midfielder's shot was blocked.
Leicester's encouraging first-half display was almost undone shortly before the break by a quick West Brom counter-attack as Stephane Sessegnon slid through Berahino, who teed up Chris Brunt on his favoured left foot but the winger fired over.
Pearson had cause for optimism at the interval but two minutes after the restart, his side fell behind.
Berahino was involved again, skipping in behind and as he cut the ball back, Morgan's attempted header away deflected back off Cambiasso and into the Leicester net.
The home side cranked up the pressure as the hour-mark approached and Vardy could have equalised when Paul Konchesky's long ball forward caught West Brom napping but after cutting back onto his right foot, the striker drove straight at Foster.
The Baggies had a strong case for a penalty when Sessegnon's chipped pass struck Wasilewski's hand but Leicester survived and Pearson threw on Ulloa for David Nugent with just over 20 minutes to play.
The Argentine almost made a telling contribution straight away as his cross from the right found Andy King in the area but the unmarked midfielder could only find Foster with his header.
Leicester continued to huff and puff in the dying minutes, bombarding West Brom's box with crosses and long throws but the visitors' defence held firm until the final whistle which was greeted with a chorus of boss from the home supporters.
Source : PA
Source: PA