Austin Healey, Ben Kay, George Chuter and Michael Holford touched down for the Tigers with Andy Goode adding three conversions and three penalties.
Irish had two tries disallowed and their only points came from an early Barry Everitt penalty.
The Exiles have now won only one of 20 matches at Welford Road while it was Leicester's first win in three games.
London Irish coach Brian Smith:
"We thought we'd scored two good tries and we were desperately disappointed they weren't given but it wouldn't have been enough.
"We expected Leicester to be very professional and physical and they dominated the tackle area.
"We had our chances early on but they were very worthy winners."
Leicester: Vesty; Lloyd, Hipkiss, Cornwell, Smith; Goode, Healey (capt); Moreno, Chuter, Morris; Hamilton, Kay; Johnson, Jennings, B Deacon.
Replacements: Rabeni for Lloyd (59), Broadfoot for Cornwell (70), Cole for Healey (70), Buckland for Chuter (70), Holford for Morris (70), Abraham for Jennings (54).
Not Used: Croft.
Sin bin: Johnson (58).
London Irish: Flutey; Staniforth, Penney, Catt, Bishop; Everitt, Willis; Hatley, Coetzee, Rautembach; Casey, Kennedy; Roche, Danaher, Murphy.
Replacements: Horak for Catt (40), Hodgson for Willis (51), Collins for Hatley (51), Russell for Coetzee (64), Skuse for Rautembach (59), Strudwick for Kennedy (64), Leguizamon for Murphy (46).
Sin bin: Russell (68).
Att: 16,815
Referee: Roy Maybank (Kent)