Danny Rose's hat-trick against nine-man Kettering saw Newport to victory.
John Dempster's foul on Sam Foley earned a penalty converted by Rose, before Adam Cunnington's straight red card for a lunge on Tommy Doherty.
A second booking saw Dempster also sent off, but Kettering goalkeeper Laurie Walker saved Rose's resulting penalty.
Moses Ashikodi turned in Marcus Kelly's cross to equalise, but Rose pounced from close range to put Newport ahead before lashing home a long-range third.
VIEW FROM THE DRESSING ROOM
Newport County manager Justin Edinburgh told BBC Radio Wales:
"We desperately wanted to get that home victory and the pleasing thing for me was we continued our good performance from Saturday.
"[Danny Rose] should have had four but he's taken his goals very well, right place at the right time, and I'm pleased for him.
"I thought that elusive goal for Craig McAllister was going to come tonight but his overall play again contributed to the victory."
Kettering Town manager Mark Stimson tells BBC Radio Northampton:
"The boys dug in and tried their best.
"We go home sad and disappointed because of the result, but also the cards will hurt us because at the moment we're running with a light squad.
"We only had 16 (players) available for today."