The former Tottenham boss was appointed as Paul Lambert's replacement on Saturday and took a watching brief as caretaker manager Scott Marshall oversaw progression thanks to goals from Leandro Bacuna and substitute Scott Sinclair.
While Sherwood will now have an FA Cup quarter-final to look forward to as he begins work on Monday, he will also likely be concerned by a Villa side that appeared short on confidence and laboured going forward prior to Bacuna's opener.
After a promising start, the hosts began to fade and could have gone in behind at the break had Marcin Wasilewsk's header gone in rather than striking Shay Given's left-hand post.
The hosts continued to frustrate the Villa Park faithful after the interval, before Bacuna justified his return to the side by beating Mark Schwarzer with Sinclair then afforded his first Villa goal courtesy of a gaffe from the goalkeeper soon afterwards.
Andrej Kramaric produced an impressive late header in a flurry of goals to give Leicester hope, but it proved scant consolation.
With new boss Sherwood watching on from the stands, Villa began brightly as Andreas Weimann scooped Alan Hutton's pass over the crossbar, although it was Leicester who had the first real opportunity.
Wasilewski - in for the cup-tied Robert Huth - headed Matty James' corner against the far post 12 minutes in as the visitors gradually got a foothold in the match.
However, much of the remainder of the opening half-hour saw the two Premier League strugglers demonstrate a lack of quality and composure in the final third. That was only punctuated by a dangerous Danny Simpson delivery that Kramaric went close to connecting with.
Referee Mark Clattenburg saw nothing wrong with Ron Vlaar's marking of Kramaric, which forced the Croatian to ground, before Given pulled off a stunning save to his left to deny James from long range.
Villa thought they had the lead when Christian Benteke fired the ball past Schwarzer, but an offside flag ensured the sides went in level at the break.
After Sherwood had ventured down to the dressing room to deliver a half-time pep-talk, Belgian Benteke was thwarted again early in the second half when he got on the end of Alan Hutton's header inside the area, only to see his effort blocked by Schwarzer.
The prolonged spell of pressure from Villa eventually paid off when Bacuna curled home a 68th-minute opener following Hutton's persistence down the left.
That prompted a flurry of late action, as first Sinclair's strike was fumbled into his own goal by Schwarzer before Kramaric demonstrated his quality to pull a goal back for the visitors late into injury time.
While Sherwood gets to work with Villa after only their third win of 2015, Nigel Pearson and Leicester now revert their focus to Premier League survival.
