City made a whirlwind start winning three corners in the first two minutes and Rovers were rarely able to get out of their own half.
Home keeper Neil Sullivan saved a first-time shot from Lloyd Dyer with his legs in the ninth minute before Waghorn fired home three minutes later.
The 20-year-old Sunderland striker raced on to a long throughball following a quick counter-attack and shook off the challenge of Gareth Roberts before giving Sullivan no chance.
Jordan Mutch fired inches wide from 20 yards when Rovers tried to hit back and Leicester had a lucky escape in the 21st minute when Billy Sharp raced through only to be brought down by Bruno Berner.
Berner was the last man and looked anxiously at the referee but was fortunate to be only shown a yellow card.
Doncaster gradually edged their way into the game with James Coppinger and Dean Shiels both having efforts saved just before the interval and they gave Leicester a taste of their own medicine in a one-sided second half.
Rovers piled on the pressure but lacked a cutting edge although they were denied several times by the reflexes of City keeper Chris Weale.
Sharp fired fractionally wide five minutes after the interval before Weale saved bravely at the feet of Sharp and Coppinger in quick succession.
Sullivan produced a fingertip save to prevent Waghorn scoring again in the 69th minute but it was otherwise one-way traffic with Weale brilliantly denying substitute Lewis Guy seven minutes from time.