Plymouth took the lead early on when Michael Kuipers could only parry Paul Wotton's cross and Danny Cullip turned it into his own net trying to clear.
Marino Keith tested Kuipers before Argyle doubled their lead, Daniel Harding being sent off for fouling Lee Hodges and Wotton scoring the penalty.
Brighton striker Maheta Molango worked hard to create chances but to no avail.
Plymouth manager Bobby Williamson:
"People have told me this is a perfect start. But that will only be the case if we get something at Cardiff on Friday," he said.
"We won't look at the league table at this stage. We'll come up against better teams but we will have to find ways of stifling them.
"If we put the same amount of effort into the forthcoming games we won't be far away."
Brighton: Kuipers, Virgo, Harding, Cullip, Butters, Mayo,
Nicolas, Jarrett (Robinson 58), Currie, Reid (Jones 45),
Molango (Hart 80).
Subs Not Used: Hinshelwood, May.
Sent Off: Harding (44).
Booked: Harding, Mayo, Currie.
Plymouth: McCormick, Worrell, Coughlan, Wotton, Gilbert,
Lasley, Adams, Hodges (Lowndes 81), Capaldi,
Crawford (Milne 68), Keith.
Subs Not Used: Larrieu, Evans, Doumbe.
Goals: Cullip 11 og, Wotton 45 pen.