Newport fielded an unchanged side to the one that had beaten Verwood Town 5-3 on Saturday.
Newport’s first good chance came in the 14th minute, when Jake Wright was unlucky to see his curling effort from the left of the penalty area skim off the Vics crossbar.
In the 26th minute, Jordan Browne had a powerful shot deflected for a corner by Vics skipper, Ryan Gregory.
This provoked a further flurry of attacks from the ‘away’ side, with Connor Kelly putting in some pinpoint crosses that deserved better finishing.
On the half hour mark, a Connor Kelly cross found Scott Barron unmarked in the middle of the penalty area, but the youngster somehow contrived to head wide when it appeared easier to score.
Against the run of play, Vics could have gone in front on 31 minutes, when a long, high ball to the back post was brilliantly headed back across goal, only for the unmarked Jordan Chapman to blast the ball wide.
Jake Wright was then presented with a second opportunity to put himself on the scoresheet when his head made contact with an inch-perfect Connor Kelly cross, but he directed his header down into the turf and up over the crossbar.
Half time: East Cowes Vics 0-0 Newport IW
The second half began with a rare scoring opportunity for Vics when a Ryan Gregory header drifted just over the crossbar.
It took until the 66th minute for the Port to convert their numerous chances into goals when a superb Joe Craig pass found the excellent Connor Kelly in the penalty area, who made no mistake as he direct the ball with pinpoint accuracy past Steinborne-Busse into the far corner of the goal.
The Port doubled their lead in the 81st minute when a Mark Taylor corner was met by the head of Scott Barron from where it flew past a huddle of defenders and landed in the back of the goal.
Newport added a third two minutes from time, when an excellent through ball by Connor Kelly found the feet of Joe Butcher for the former Vics stalwart to send a low shot past Steinborne-Busse to complete the comprehensive victory for the ‘away’ side.
Full time: East Cowes Vics 0-3 Newport IW
Newport: Streeter, Hughes, Lamb, Przespolewski (Reynolds 80), McDonough (c), Barron, Kelly, Wright (Taylor 70), Younie (Butcher 69), Browne, Craig.
Subs not used: McCormack, Pearce
Report: Warren Whitmore