The ex-Carmarthen Town striker's clever movement caused trouble from the start and he gave Wrexham the lead with an unstoppable 20-yarder before the break.
Marc Williams drove in a fierce strike, 22-year-old Mohamed added a glancing header, and Williams tapped in as the Welsh side ran riot after the break.
Shane McCabe got a late consolation strike for the Swifts.
Dungannon: Dwayne Nelson, Mark McConkey (Niall McGinn 58), JP Gallagher (Dwayne McManus 64), Adam McMinn, Gary Fitzpatrick, John Curran (Finbar Hefferman 84), Shane McCabe, Michael Hegarty (Mark Magennis 76), Shea Campbell, Mark McAllister (Paul Baron 74), Terry Fitzpatrick.
Subs: Anthony Williams.Att 200.
Match report from the official website here