The England flanker rounded off a quality Tigers display by claiming his team's third try - a 50-metre solo effort complete with one-handed finish - that ended Quins' reign as English champions.
Leicester now face a Twickenham clash against Saracens or Northampton on May 25 after wrestling control when Quins' England scrum-half Danny Care received a yellow card.
With the dangerous Care out of commission, Tigers wing Niall Morris crossed for a try that followed Vereniki Goneva's first-half touchdown, and Leicester were home and dry.
Full-back Mathew Tait, who ran Croft close as Leicester's most effective performer, added a fourth try, while fly-half Toby Flood chipped in with 13 points from three penalties and two conversions.
Quins were left to reflect on three Nick Evans penalties and a late Ross Chisholm try that Evans converted as their sole crumbs of comfort.
Ultimately, they were horribly overpowered by a Leicester side that scored 27 unanswered points from 9-6 adrift just before the break and Quins had no answer.
The Londoners, knocked out of Europe at home by Munster last month, had been chasing three major trophies this term, but they will end it with just the LV= Cup in their possession.
Robshaw's absence meant Luke Wallace continued in the Quins back-row, while his fellow flanker Maurie Fa'asavalu replaced Tom Guest and hooker Joe Gray was preferred to Rob Buchanan following a narrow victory over Northampton last time out.
Leicester, meanwhile, showed two changes from the side that defeated London Irish seven days ago, with full-back Mathew Tait and prop Dan Cole both returning to action.
Tigers drew first blood when Flood struck a third-minute penalty, but Quins then assumed a degree of control with Care snapping away at his forwards' heels.
Cole conceded a penalty that Evans landed from short range and the New Zealander was on hand again just seven minutes later to put Quins 6-3 ahead before Flood missed an attempted equalising strike from 45 metres.
England hooker Tom Youngs made a couple of midfield surges for the home side, but Quins checked any danger and then went close to extending their lead after 27 minutes.
Prop James Johnston was held just short of Leicester's line and Care looked certain to score when he secured possession just two metres out, but Croft responded through a stunning reflex tackle that saw him nudge possession from his England team-mate's hands.
Evans completed his penalty hat-trick eight minutes before the break and although Flood soon cancelled that out, Quins looked to have done enough for an interval advantage.
Leicester, though, had other ideas and they stunned their opponents through a long range counter-attack sparked by Ben Youngs finding number eight Jordan Crane after Quins full-back Mike Brown lost possession in contact.
Crane freed Goneva on the left-hand touchline and he finished superbly, brushing off Tom Williams' attempted tackle to score a superb try that Flood converted, putting Tigers 13-9 in front.
It gave Leicester the confidence to pin Quins back from the restart, and they received an unexpected bonus when Care was sin-binned.
Referee Greg Garner ruled that Care deliberately knocked on Leicester possession following a breakaway by Tait, and although it appeared a harsh call, Quins were down to 14 men for 10 minutes.
And Leicester made them pay, scoring 10 unanswered points while Care was off when Flood kicked a penalty and converted Morris' try.
Care then returned, but within a minute Leicester were out of sight after Croft left Quins' defence for dead through a searing burst that ended the game as a contest.
Quins were then faced with a painful damage-limitation exercise as the clock ticked down, but there was still time for Leicester to inflict one more wound as Tait crossed eight minutes from time.
Chisholm had the final say, yet it was a day when Leicester once again flexed their collective muscle as true English heavyweights that should install them as title favourites.
- Sports & Recreation
- Mathew Tait
- Danny Care