Danny Webber scored a consolation for Stanley but that failed to stop the party mood in south east Wales following Newport's first game back in the top four divisions since they faced Rochdale on May 7, 1988.
Burton hit back from two goals down to draw 2-2 at Cheltenham.
York made a winning start to the new season following a late 1-0 victory over 10-man Northampton.
Chesterfield ensured Bury's revolution got off to a disappointing start by clinching a 2-0 win at Gigg Lane.
Paris Cowan-Hall scored within seven minutes of his Wycombe debut as the Chairboys began the new season with a 1-0 defeat of Morecambe.
Fleetwood cruised to a 3-1 home win over Dagenham and Redbridge, as did Rochdale by a score of 3-0 against Hartlepool at Spotland.
Torquay and AFC Wimbledon shared the spoils in a 1-1 draw, and Southend edged out Plymouth 1-0.
Portsmouth, fresh off yet another relegation, took the lead at home to Oxford United but ended up losing 4-1 after having Johannes Ertl sent off.