Central defender Morgan scored in consecutive games for the first time in his Leicester career, although there may have been a touch of fortune about his deflection which went in off the post from Ben Chilwell's 11th minute shot.
An entertaining match saw both teams' top strikers, Vardy and Callum Wilson, miss chances but Leicester, increasingly dominant, deserved the spoils when Vardy headed home his fifth goal in five games eight minutes from time.
It felt a fitting way for Leicester fans to honour Srivaddhanaprabha, their much-loved Thai owner who died in a helicopter accident after a game in October, on what would have been his 61st birthday.
Before the game, his image flashed up on the big screen at the King Power Stadium along with the words 'Always in our hearts' and Srivaddhanaprabha's son, club chairman Aiyawatt, was introduced to the crowd.
In the 61st minute of the match, the fans also rose to applaud his memory, singing 'Vichai had a dream.'
Leicester had also arranged for fans to be given free cake and beer to mark the day and the home players responded with a fine performance.
"I thought we were excellent. We had to work hard, it was a real good test, we were outstanding on the back of the international break," said Rodgers.
"Our pressing was excellent, the boys are understanding tactically how we want to press and the importance of that... We had 18 shots on goal, which is a real positive."
The Northern Irishman also said he was also impressed with the contribution of Vardy, who has scored four times in four games since Rodgers took over the managerial reins from Claude Puel.
(Reporting by Ian Chadband; Editing by Christian Radnedge)
