Assistant manager Daren Dykes admitted Newport Pagnell Town were poor in the first half, but did enough to see off Bugbrooke 3-1 in the FA Vase.
Bugbrooke provided a potential banana skin, performing well in the league below Swans, but things looked to be going to plan when Josh Crawley put the home side ahead.
“After that we really did create our own problems which gave them the equaliser,” said Dykes. “Take nothing away from Bugbrooke though because they battled well and made it tough for us to get the ball down and play.
“We came in at 1-1 and knew that once we had a chat and sorted a few tactical issues out we would go on and win.”
From there, Newport didn’t look back. Crawley netted hit and the team’s second before Dom Lawless wrapped things up.
Newport will now play Berkhamstead in the second round on Saturday October 4.
They play Wellingborough at Willen Road on Saturday.
In UCL Division 1, Olney Town suffered their third defeat of the season, going down 2-0 to Bourne Town at home.
Stony Stratford Town returned to winning ways in South Midlands Division 1, beating Arlesey Town Reserves 4-0.
Willen moved off the foot of Division 2 wit ha thumping 5-1 win over Aston Clinton, while Wolverton Town were on the wrong end of the same score to The 61 FC (Luton).
New Bradwell St Peter were 4-0 winners over Corinthians, Old Bradwell picked up a point on the road against Totternhoe, drawing 0-0, but Mursley United were beaten 4-0 by Kent Athletic.