The 23-year-old fly-half, who has four Wales caps, sprained an ankle in a win over Cardiff Blues on 1 January.
Scarlets earned a bonus point before half time thanks to further tries from Wyn Jones and Olympian James Davies.
Edinburgh have won only one of their last 10 matches in the Pro12 and only four games all season.
Scarlets head coach Wayne Pivac named seven returning internationals after the conclusion of the Six Nations, while Edinburgh welcomed back nine Scotland players.
But it was Wales hopeful Patchell who boosted his chances of selection for Wales' summer tour in which they face Samoa in Apia and Tonga in Auckland.
Scarlets were be looking to bounce back following a disappointing defeat to Leinster in the last round and made the perfect start when Hadleigh Parkes' sensational dummy allowed Patchell to pounce and score after a surging run.
Duncan Weir reduced the arrears for Edinburgh with a penalty, but the Scarlets then powered over, a driving line-out resulting in prop Wyn Jones crossing for the second try in the opening 15 minutes.
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Parkes was again the instigator as James Davies surged clear for the Scarlets' third try, his perfectly weighted pass splitting open the Edinburgh defence and giving Davies an easy run in through the gap.
However, the hosts gave Edinburgh a gift of a reply, a charged down kick rebounding kindly into the path of Phil Burleigh who went over, with Weir adding the extras.
The Scarlets had however, secured a bonus point by the 30 minute mark when Patchell again found space and was able to cross the whitewash for try number four.
Patchell was withdrawn to a standing ovation on the 50 minute mark, replaced by Dan Jones, with the contest petering out as the Scarlets looked to protect what they had.
Scarlets rang the changes throughout the second period, introducing Emyr Phillips and DTH van der Merwe, but they lacked execution to match their industry and a slew of handling errors restricted the contest to no further scores.
Scarlets head coach Wayne Pivac:
"We created some opportunities [in the second half] but just didn't get to finish them off. Certainly to get four tries by half time is half the job done.
"We talked at half time and we needed to go on and score first and it didn't happen.
"After a few weeks off we were a little bit slow to finish them off."
Scarlets: Johnny McNicholl; Liam Williams, Jonathan Davies, Hadleigh Parkes (capt), Steff Evans, Rhys Patchell; Aled Davies, Wyn Jones, Ryan Elias, Samson Lee, Tom Price, Tadhg Beirne, Aaron Shingler, James Davies, Will Boyde.
Replacements: Emyr Phillips, Rob Evans, Werner Kruger, Lewis Rawlins, John Barclay, Gareth Davies, Dan Jones, DTH van der Merwe.
Edinburgh: Blair Kinghorn, Damien Hoyland, Chris Dean, Phil Burleigh, Tom Brown, Duncan Weir, Sam Hidalgo-Clyne, Allan Dell, Ross Ford (capt), Simon Berghan, Anton Bresler, Ben Toolis, Viliame Mata, Jamie Ritchie, Cornell Du Preez
Replacements: Stuart McInally, Murray McCallum, Kevin Bryce, Grant Gilchrist, Viliami Fihaki, Nathan Fowles, Jason Tovey, Glenn Bryce.
Referee: John Lacey (Ireland)
Assistant referees: Gary Conway (Ireland), Wayne Davies (Wales)
TMO: Kevin Beggs (Ireland).
Wales fly-half Rhys Patchell scored two tries within thirty minutes of his return after three months out injured as the Scarlets beat Edinburgh 26-10.