Eriksson was handed a substantial transfer kitty by Leicester's Thai owners during the close-season and splashed out over £8 million on 10 new signings.
The spending spree paid instant dividends as Leicester recovered from Darius Vassell's early dismissal to take the points thanks to defender Lee Peltier's goal soon after half-time at the Ricoh Arena.
Coventry were also down to 10 men by then after Carl Baker saw red for a reckless challenge.
The Asia Football Investments consortium, fronted by Vichai and Aiyawatt Raksriaksorn, have set Eriksson a target of promotion to the Premier League this season and this gritty victory gave the former England coach encouragement for the hard work ahead.
Eriksson handed debuts to seven of his new arrivals, with Peltier, David Nugent, Kasper Schmeichel, Paul Konchesky, Gelson Fernandes, Neil Danns and skipper Matt Mills all starting.
The Foxes got off to the worst possible start when former England striker Vassell was given his marching orders for a studs-up challenge on Richard Keogh.
Coventry threatened to take advantage when Schmeichel was tested for the first time in the 37th minute as he tipped David Bell's long-range effort over the bar.
But within two minutes Coventry's numerical advantage was wiped out as Baker saw red for a needless foul on Richie Wellens.
Leicester took charge fter that and came close to breaking the deadlock when Nugent headed Danns' cross against the inside of a post.
They finally made the breakthrough in the 52nd minute as Wellens produced a perfectly weighted cross that Peltier headed past Joe Murphy to seal the points.
Source: AFP
Source: AFP