Scottish winger Matt Williams' early touchdown caused shudders round a soaking wet Sixways.
But the home side responded with four tries, allied to 18 points from the boot of stand-off Ryan Lamb.
Flanker Sam Lewis scored a hat-trick of tries, while winger Dean Hammond also crossed the whitewash.
Lamb kicked three of his four conversion attempts, as well as two key first-half penalties - and two more late in the game.
Full-back Peter Lydon got the Exiles' other try, which he converted, along with a first-half penalty for a 10-point haul.
Scottish trailed by five points from Saturday's first leg, only for that advantage to be wiped out inside the first six minutes.
Jamie Stevenson's blindside run set up right wing Williams to score in the corner.
But that turned out to be the nearest this contest got to a Scottish gain as Warriors eventually rallied and started to tick the right boxes.
Two Lamb penalties in the space of three minutes were followed by a Sam Lewis pushover try in the left corner, from which Lamb was also successful with the conversion.
Peter Lydon did reduce the deficit at the interval to 13-8 with a penalty, but two tries in four minutes at the start of the second half killed the contest.
All Blacks winger Cooper Vuna, switched to full-back following an early injury to Ben Howard, set up Hammond, converted by Lamb before Lewis crashed over in the right corner, from which Lamb missed his first kick of the night.
Lydon converted his own try to bring it back to 25-15 on the night, before Lewis's third try, again converted by Lamb.
Lamb landed two more penalties before injury-weakened Warriors brought the biggest roar of the night with the late introduction of 17-year-old schoolboy Jamie Shillcock at scrum-half.
Warriors: Howard; Hammond, Grove, Mills, Vuna; Lamb, Bruzulier; Rapava Ruskin, Creevy, Schonert, Percival, Thomas, Mike Williams, Lewis, van Velze (capt).
Replacements: Annett, Fainga'anuku, Rees, Cox, Shillcock, Fatiaki, Biggs.
London Scottish: Lydon; Matt Williams, Moffat, Gidlow, Doneghan; Newton, Stevenson; Lilley, Kwasnicki, Prescott, Phillips, Thomas Brown, Gillanders, Best, Bright (capt).
Replacements: Hallam, Stephenson, Rae, Chisholm, Walker, Heeks, Millar.
Attendance: 6,658
Worcester Warriors booked their place in the Championship play-off final, but they had to come from behind to beat London Scottish on the night.