The home side scored five tries to one, with three of their five-pointers coming in the first half as they racked up a useful 25-6 half-time lead.
Gordon Ross put his side ahead by 3-0 after just six minutes, but 'new' Leicester signing Andy Goode – back in Tigers' colours after switching from Saracens just a few days ago – drew level at 3-all just four minutes later.
Ross and Goode traded one more penalty each to leave the score at 6-6, but the home side had suffered a huge setback before Ross's second penalty when centre Leon Lloyd was sin-binned for a high tackle in the 17th minute.
But Leicester's defence held out with Lloyd in the bin and Healey scooted over in the 29th minute, with Goode converting to give the home side a handy 13-6 lead.
Thirteen points to six soon became 25-6 shortly before half-time when discarded England loosehead prop Graham Rowntree got over for a try from a typically powerful Leicester rolling maul. Samoan back Freddie Tuilagi scored Leicester's third try – after smart work from Jaco van der Westhuyzen and Ollie Smith – with Goode's conversion from out wide making up for his missed effort after Rowntree's score.
Club skipper Neil Back scored from another powerful Leicester maul shortly after the break to give the home team their fourth-try bonus point, Goode again adding the two points as the Tigers ran into a 32-6 lead.
Former Wales fullback Matt Cardey grabbed a consolation score for his side – after looping around to create an overlap – but Leicester wing Neil Baxter had the final say when he touched down in the 80th minute after a break from Goode, who had the final say with his fourth conversion.
For Leicester Tigers:Tries: Healey, Rowntree, Tuilagi, Back, BaxterCons: Goode 4Pens: Goode 2
For Leeds Tykes:Try: CardeyPens: Ross 2