Wiegman said she would make changes from Friday's win in Greece and opted for two, shaking up the defence with Jess Carter coming in, while talented 20-year-old Potter made her full debut.
It made a difference as Potter's introduction allowed experienced midfield duo Stanway and Keira Walsh to push higher up and cause plenty of problems.
Walsh and Potter teamed up to reduce Greece's threat on the counter-attack, though the visitors still managed to test England's defence, which looked vulnerable at times.
Goalkeeper Hannah Hampton was called into action on a few occasions early on but England settled quickly and did the job very convincingly at the other end.
Wiegman had called for more ruthlessness after her side misfired in Crete and she was given the perfect response by her players.
Stanway now has an impressive 11 goals in her past 10 England matches, while Chelsea's James was in electric form in an entertaining first half that rewarded her with two goals.
England's number nine Russo was also sharp and set the tone within three minutes, allowing the hosts to gain confidence and build momentum, with the crowd chanting "we want six" in stoppage time.
By getting the job done in the first half, Wiegman was able to make changes and handed a debut to London City Lionesses forward Freya Godfrey and valuable minutes to full-back Niamh Charles.
Stronger opposition will come as they gear up for a potentially big 2027 - but with Ukraine up next in the play-offs, England should be confident of progressing.
They beat Ukraine in both matches in the league phase, winning 9-1 on aggregate, and have shown they do have a ruthless streak that will strike fear into any opposition.