Eriksson, installed as Paulo Sousa's successor at the Walkers Stadium earlier this month, saw his new charges turn on the style with a display full of verve that was too good for Leeds by a considerable distance.
The Foxes, who could have been 4-0 up in the first 20 minutes, had to wait until the 63rd minute before converting their superiority into goals when Naughton, on-loan from Tottenham, capitalised on some kamikaze defending to open the scoring.
Howard slid home Leicester's second on the break in the 81st minute and although Luciano Becchio set up a grandstand finale by heading home two minutes later, it was too little too late for Leeds, who slipped to their third home defeat in six league matches.
Eriksson's first match in charge on Saturday ended in a 1-1 home draw with Hull, and his players were full of running at Elland Road.
Grayson named the same side that kicked off Saturday's 2-1 win at Middlesbrough, while Eriksson recalled Franck Moussa and opted to start with Howard on the bench.
Leicester threatened to open the scoring at the Kop End in the eighth minute when Martyn Waghorn played in Andy King, but the Foxes midfielder dragged his shot inches wide.
The same pair combined two minutes later, this time Waghorn curling his shot over the crossbar and within another 60 seconds Paul Gallagher blazed his volley off target when found unmarked by Moussa's cross.
Leeds were at sixes and sevens as Leicester swept forward and only alert goalkeeper Jason Brown, who tipped Bruno Berner's 25-yard thunderbolt on to the crossbar, prevented the visitors taking a deserved lead.
It took Leeds 26 minutes to muster their first effort on goal when Richard Naylor headed Jonny Howson's cross wide.
Grayson had seen enough by the half-hour mark, withdrawing wide midfielder Sanchez Watt and replacing him with Bradley Johnson in a more central role.
Johnson mistimed his header soon after, but the switch helped Leeds stem the tide and the same player crashed a 20-yard shot high and wide after Becchio's lay-off just before the break.
Leeds began the second period in a much more positive vein and a period of pressure culminated in Becchio heading powerfully wide from a corner.
But Leicester broke the deadlock in the 63rd minute. Leeds left-back George McCartney made a hash of his tackle on Naughton on the edge of the penalty area and the Foxes defender ran on, firing goalwards and seeing his shot loop over Leeds goalkeeper Brown and into the net after taking a deflection off centre-half Neill Collins.
Eriksson replaced Moussa with striker Howard in the closing stages and within minutes the veteran put his side two goals to the good after a neat interchange with King.
Becchio headed home his sixth goal of the season from substitute Max Gradel's cross with seven minutes remaining, but it would have been rough on Eriksson's Foxes if Leeds had denied them three points.