A crowd of almost 10,000 saw Gloucester have the game won by the interval before sloppy play allowed the Welsh to compete more favourably in the second half.
Morgan and Freddie Burns, who were both released from the England squad for the game, were at the heart of the action.
Number eight Morgan claimed his try haul and also impressed with driving runs, while Burns was creative and collected 14 points with the boot.
Gloucester fielded a strong line-up, and apart from Burns and Morgan, Jimmy Cowan was at half-back with Mike Tindall and Billy Twelvetrees forming a threatening centre partnership.
The hosts suffered a blow in the first minute when Rob Cook was sin-binned for a dangerous tackle, but they then had the first chance for points when Exiles number eight Adam Balding was penalised for a high tackle on Tindall and Burns made no mistake with his kick.
After seven minutes Gloucester scored their first try, Twelvetrees making a huge dent in the Welsh defence to send Steph Reynolds deep into the visitors' 22.
The ball was quickly recycled for Shane Monahan to crash over for a try which Burns converted.
Two penalties from Gordon Ross reduced the Welsh deficit to 10-6 at the end of the first quarter but soon afterwards a powerful line-out drive from the home pack resulted in a try for Morgan. Burns converted this and added a penalty goal.
Gloucester declined three kickable penalties in favour of more attacking options and were rewarded with a close-range try from Akapusi Qera.
That occurred immediately after Welsh lock Matt Corker was sin-binned by Tim Wigglesworth as the referee finally lost patience with the visitors' frequent attempts to kill the ball.
Welsh were further hit when centre Seb Jewell was helped off with a leg injury, and three minutes before the interval Gloucester scored an excellent team try through Morgan following a 70-metre move.
Burns' fourth conversion made it 34-6 at half-time and the game was already over as a contest.
As a result Gloucester withdrew influential forwards Qera and Will James at the interval.
It made no immediate difference as the hosts continued to dominate. The first 10 minutes of the half saw them camped in the opposition 22, but greedy choices from individuals and over-elaboration prevented them from extending their advantage.
It took the Welsh 10 minutes of the second half to get out of their own half but a much better tackling effort had considerably frustrated Gloucester.
The visitors gained reward for their improved performance with their first try from Nick Scott which was converted by Ross to make it 34-13.
Burns and Twelvetrees left the action just in time to view replacement Koree Britton scoring the fifth Gloucester try before man of the match Morgan scored his third try five minutes from the end.
Welsh had the final say when a glaring error from Tindall gifted a try to replacement prop James Tideswell.
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