Shrimps midfielder Andrew Fleming fired home in the 14th minute before his 35-yard lob 10 minutes later doubled the visitors' lead at St James' Park.
Izak Reid then sealed the win just after half-an-hour in a convincing display for the travelling side.
Rotherham were also on form in their opening league fixture as they beat 10-man Burton Albion 3-0 at the New York Stadium.
Daniel Nardiello converted a penalty in the fifth minute when he was brought down by Zander Diamond before Kayode Odejayi headed the Millers into a two-goal lead six minutes later.
Ben Pringle finished things off with a strike from the right of the area in the 75th minute as the south Yorkshire side took their place in the top three, with Lee Bell seeing red for Burton for two bookable offences.
Port Vale also won by a 3-0 margin at home to Barnet.
Louis Dodds opened the scoring in the eighth minute before Jennison Myrie-Williams doubled the lead from the penalty spot soon after when Barnet striker Jonathan Nurse fouled Tom Pope.
Pope wrapped up the comfortable victory with his strike in the 75th minute.
Meanwhile, Bristol Rovers slumped to a 2-0 defeat by Oxford United at the Memorial Stadium.
Jake Forster-Caskey scored first for the U's with a 20-yard curling shot before Alfie Potter drilled the second in the 32nd minute.
Cheltenham beat Dagenham and Redbridge 2-0 in their match at Whaddon Road.
Shaun Harrad edged the Robins ahead in first-half injury-time with Jermaine McGlashan securing all three points four minutes into the second half with a 30-yard strike.
Danny Kedwell scored twice at the Priestfield Stadium as Gillingham powered past Bradford 3-1.
Kedwell volleyed the opening goal from the right byline just before half-time then doubled his tally from the penalty spot when Bradford's Garry Thompson brought down Charlie Lee in the box.
Nahki Wells pulled one back for the visitors from the spot after he was fouled by Andy Frampton, but the Gills soon re-established their two-goal lead when Myles Weston scored with two minutes left on the clock.
Newly-promoted York suffered a disappointing start to their season as they were beaten 3-1 at home by Wycombe.
Matt Bloomfield, Sam Wood and Gareth Ainsworth all scored for the Wanderers with Jason Walker's 54th-minute reply not enough in a comfortable game for the visitors.
Plymouth were beaten 2-0 at home by Aldershot thanks to Troy Brown's header and Josh Payne's penalty while Karl Sheppard's 61st-minute goal saw Accrington Stanley beat Southend at Roots Hall.
Elsewhere, Fleetwood and Torquay drew 0-0, Rochdale and Northampton also played out a goalless draw while Jack Midson's first-half goal was enough for AFC Wimbledon to beat Chesterfield 1-0.