But the Tigers were still given a scare by prolific Irish goalkicker Barry Everitt who keep the visitors reined until the final quarter.
Corry's try, one of the fastest in Premiership history, following a handling blunder by his opposite number Kieran Roche, and gave Leicester the perfect start.
It got better just eight minutes later when Tigers' Fijian wing Seru Rabeni waltzed over from close range, suggesting that Irish were in for a tough afternoon despite holding an early one-man advantage when former England captain Martin Johnson was sin-binned.
Johnson's spell on the sidelines lasted almost 14 minutes, instead of the regulation 10, for no obvious reason, but when he eventually returned, Leicester just could not stop conceding penalties.
Everitt, after an early strike, kicked four further penalties between the 20th and 39th minutes as Irish briefly led 15-12.
And it took a flash of individual brilliance from Leicester's Irish international full-back Geordan Murphy to resume normal service.
Murphy ran powerfully out of his own half and kicked ahead towards the Irish line. Although the home side got defensive numbers back, it was not enough as Tigers' flanker Brett Deacon supported Murphy and dived over.
Fly-half Andy Goode, who finished with 19 points, slotted the conversion and Leicester trooped off at half time with their noses just in front following a fast and furious opening period.
Leicester, who uncharacteristically failed to win a trophy last term and only just sneaked through the Heineken Cup qualification door, mean business under coach John Wells.
Although Irish had their moments, and Everitt kicked six out of six shots at goal to finish with 17 points, the visitors always looked capable of stepping up a gear.
A Goode penalty on 52 minutes opened up a 22-15 advantage before the fly half administered what was a telling scoring blow.
A superb Leicester move was started by Goode's slashing midfield break, and outstanding support work from flanker Neil Back and hooker George Chuter enabled the move to continue and Goode rounded it off with a try that gave Leicester a bonus point.
Australian Scott Staniforth, comfortably Irish's most dangerous attacker, gave the home side a glimmer of hope with a well-worked 63rd minute touchdown, but Leicester were in no mood to give anything away.
Former England flanker Back was again heavily involved in Leicester's fifth and final try, which was scored by wing Austin Healey after some intricate passing between Corry, Back and scrum half Harry Ellis.
Goode added the conversion and then kicked a 75th minute penalty, and although Leicester finished with Chuter in the sin bin – like Johnson, he was yellow carded for a technical offence – it made no difference to the final outcome.
Leicester, with confidence high, can now look forward to a sell-out Midlands derby against Northampton next Saturday, but Irish, on the back of two successive league defeats, face a tall order when they visit reigning champions Wasps.
For London Irish:Try: Staniforth Con: Everitt Pens: Everitt 5
For Leicester Tigers:Tries: Rabeni, Corry, Goode, Deacon, HealeyCons: Goode 4 Pens: Goode 2
Yellow cards: M Johnson (Leicester Tigers, 6), Chuter ((Leicester Tigers, 76)