The Port made a couple of changes to the starting line-up that had won 5-2 at Ringwood on Saturday with Spike Pearce replacing Martin McDonough in central defence and Jacob Reynolds taking the place of Jake Wright in midfield.
Newport began the game with attacking intent with Joe Butcher sending a low cross across the face of the goal as early as the first minute, but no-one was there to take advantage of the opportunity.
The Port scored in just the fifth minute of the game when a superb cross by the ever-dangerous Connor Kelly was met by the flying head of Jacob REYNOLDS.
The home team came close to extending their lead two minutes later when Connor Kelly rounded the Baffins keeper but was unable to convert the chance from a tight angle.
The Port found themselves two-nil up in the 22nd minute when Jordan Browne put Joe BUTCHER through for the powerful forward to send a precision strike past the Baffins keeper.
Baffins pulled a goal back in the 24th minute after Scott Barron made a clumsy challenge in the Port penalty area, which was gratefully converted by Tommy SCUTT.
HT Newport 2-1 Baffins Milton Rovers
The visiting Wessex Premier League side began the second half full of attacking intent with a flying tackle by Spike Pearce preventing Baffins from equalizing early in the second half.
The start of the second half was marred by what appeared to have been a serious injury to one of the visiting players, Charlie Osborne.
Osborne’s replacement, Rudi Blankson, proved to be a very powerful forward, who was more than difficult for the Port defence to contain.
BLANKSON scored in the 54th minute, when he knocked in a shot that Gary Streeter had blocked but not held.
The game was then held up following a second serious injury to the Baffins player, Callum Dart.
Baffins then took the lead in the 72nd minute with a magnificent individual goal by the dangerous BLANKSON, who powered his way past two defenders before placing a low shot past Gary Streeter.
The Portsmouth side came close to extending their lead a few minutes later but a superb flying tackle by Spike Pearce rescued the Port for a second time.
Newport then proved to higher division opposition that they are not to be underestimated. First, substitute Jake Wright shot just over the crossbar in the 82nd minute.
Then, Scott BARRON got his head to a curling cross by Alec Przepolewski to equalize for the Port.
Finally, in the fourth minute of injury time, substitute, Jared Cousins, was spectacularly upended in the Baffins penalty area and Connor KELLY coolly converted the resulting spot kick to deliver the coup de gras to the Port’s Premier Division opponents.
Newport now face Bashley in the third round of the Wessex League Cup.
Newport: Streeter, Hughes, Lamb, Przepolewski, Pearce, Barron, Kelly, Reynolds (Wright), Butcher (Cousins), Browne (capt), Younie (Craig)
Referee: A Wright