Derek Niven, Colin Larkin and Paul Shaw scored the goals to secure the success at Dean Court.
Vale cruised to the points over newly-promoted Leyton Orient, Leon Constantine netted a brace with Akpo Sodje completing the scoring.
Cheltenham Town, promoted via the League Two play-offs last season, pulled off a shock with a 2-1 win at Swansea City.
Kayode Odejayi put the Robins ahead, and Grant McCann doubled their advantage. Leon Knight got the consolation for the Swans.
Carlisle took just four minutes to take the lead against Doncaster, with Paul Murray firing the Cumbrians ahead at Brunton Park.
But they had to battle hard at the back to keep the Yorkshire side at bat, with Rovers unlucky not to force an equaliser.
Nottingham Forest showed signs of coping with the burden of expectation better than they did last season with a 1-0 home win over Bradford.
Defender Julian Bennett scored the only goal of the game 10 minutes in.
Millwall struggled to adapt to life in League One following their summer relegation from the Championship, with them stumbling to a draw with Yeovil at the New Den.
Wayne Gray put the Glovers ahead, with Darren Byfield grabbing an undeserved leveller eight minutes from time.
Crewe Alexandra twice let a lead slip against Northampton at Gresty Road, eventually drawing 2-2.
Ryan Lowe and David Vaughan scored for the Alex, with Scott McGleish and Andy Kirk striking for the Cobblers.
Rotherham's fight for survival got off to a bad start with a lacklustre home loss at the hands of Brighton - with Alex Revell scoring for the Seagulls.
Brentford and Tranmere were single goal winners over Blackpool and Oldham respectively.
Gillingham were 2-1 winners over Huddersfield at Priestfield, with Matthew Jarvis and Dean McDonald scoring the goals - Gary Taylor-Fletcher pulled one back for the Terriers after 81 minutes.