Murphy headed home from Max Kretzschmar's corner to become the fifth debutant in as many seasons to find the net on the opening day, before birthday boy Sam Wood waltzed past two defenders before laying on a well-timed lay-off for Cowan-Hall to sidefoot home.
Newport enjoyed plenty of possession in the second period but found chances hard to come by, as the Blues celebrated a clean sheet on the day that Brentford defender Alfie Mawson made a superb debut just hours after his month-long youth loan at the club was announced.
Mawson's inclusion came following news that Gary Doherty will be sidelined for eight weeks with a knee injury sustained in a challenge at Barnet, while Danny Rowe was kept on the bench after picking up a knock in training.
Meanwhile, Josh Scowen and Stuart Lewis were unable to recover from their pre-season niggles in time, giving Murphy the chance to make his debut alongside Max Kretzschmar in midfield, with Paul Hayes captaining the side alongside Matt McClure up-front.
A smart move from the Blues forced a corner in the opening minutes of the game and Aaron Pierre came close to a dream start, thumping a header goalwards which keeper Lenny Pidgeley did well to save.
Michael Flynn twice tested Matt Ingram and Kevin Feely headed over as the hosts looked to assert their authority, while efforts from distance from Kretzschmar and Joe Jacobson served as a reminder that the visitors had attacking intentions of their own.
And it was Kretzschmar who played a vital role in the opening goal, sending a well-measured corner into the fray where Murphy lost his man and directed his header into the back of the net, celebrating wildly in front of the away fans after giving his new side the lead.
But if those fans were happy with their one-goal lead, they were delirious moments later when a dazzling passage of play sent Sam Wood into the box, and after beating a couple of defenders with some quick footwork, he laid the ball off for Cowan-Hall to complete the move with a composed finish.
County were stunned and left the field to boos at half-time, but began the second period on the front foot and saw Rene Howe head wide before Lee Minshull's header bounced past the far post after Howe's flick-on.
The new-found height in the Wycombe backline was evidently a huge factor in their ability to keep Newport at bay, snuffing out attacks with relative ease as Mawson and Pierre performed beyond their years with a blend of brave blocks and composed defending to prevent the home side getting back into the game.
Robbie Willmott curled a free-kick wide from a dangerous position while Sam Wood fired wide in a rare attacking foray in the second period, but by that point the game looked won thanks to a real team effort of closing the opposition down and maintaining the shape which had put them in such a position in the first place.
Six minutes of injury time came and went and the excellently vocal away fans were able to celebrate what is a second consecutive away win, albeit in very different circumstances from the success at Torquay 14 weeks ago.
Blues: Ingram, Jombati, Jacobson, Mawson, Pierre, Cowan-Hall (Craig 88), Murphy, Kretzschmar (Bloomfield 81), Wood, Hayes (c), McClure.
Subs: Richardson, Rowe, Morias, Walker, Holloway.
Newport: Pidgeley, Willmott, Sandell, Feely, Jones, Minshull (Chapman 73), Flynn (Yakubu 58), Byrne, O'Connor (Klukowski 58), Zebroski, Howe.
Subs: Thomas, Jeffers, Hughes, Jolley.
Referee: Mr P Bankes
Attendance: 3,736 (away crowd unknown)