Right-back Lee Peltier, Eriksson's first of 10 signings this summer, grabbed the vital breakthrough in the 52nd minute as he nodded home an inch-perfect cross from Richie Wellens.
But the encounter was shaped by the first-half dismissals of Darius Vassell and Carl Baker - one apiece for both sides - for reckless challenges which left referee Darren Deadman no option but to brandish red twice.
Nevertheless, for Leicester - who also hit the post through David Nugent - it was a winning start to a campaign which promises plenty having been bankrolled heavily over the summer by Thai-based Asia Football Investments consortium, fronted by Vichai and Aiyawatt Raksriaksorn.
The Foxes' ambitious campaign which got off to the worst possible start when Vassell was rightfully given his marching orders for a studs-up challenge on Richard Keogh near the halfway line.
The former England striker's dismissal certainly raised the tails of unfancied Coventry but it was the visitors, however, who almost opened the scoring midway through the first half as Nugent drilled an effort across goal which narrowly eluded Neil Danns.
Six minutes before half-time Coventry's numerical advantage was wiped out as Baker saw red for another needless challenge on Wellens.
The swing of the game changed almost immediately and Leicester came closest to breaking the deadlock as Nugent headed Danns' cross against the inside of a post and watched as the ball fortunately fell straight into the arms of Murphy, with the visitors finishing the half the stronger.
Leicester started the second half where they finished the first and a well-placed Nugent should have done better from Paul Konchesky's cross but he could only fire wide. But he was reprieved shortly after as Wellens succeeded where Coventry had failed - with a great delivery into the penalty area - which was met by the head of Peltier.
Eriksson's charges looked more likely to add to their opener as the second half wore on but Sky Blues skipper Sammy Clingan reminded the visitors of their own threat with a 72nd-minute effort which was parried by Kasper Schmeichel.
Source: PA
Source: PA