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."
Newport County 01 Potter 05 Warren 16 Hughes 17 Hatswell 25 Rodgers Booked (Miller - 67' ) 07 Rose 14 Doherty (Rogers - 64' ) 19 Pipe Booked (Jarvis - 80' ) 09 McAllister 10 Foley 11 Knights Substitutes 18 Thompson 04 Miller 08 Rogers 27 Jardim 15 Jarvis Kettering 12 Walker 03 Davis Booked 05 Sangare 21 Koo-Boothe 25 Dempster Dismissed after an earlier booking 08 Aman (Bridges - 69' ) 11 Kelly 16 Meechan Booked (Ifil - 46' ) 33 O'Leary 07 Ashikodi (Dawkin - 57' ) 24 Cunnington Dismissed Substitutes 31 Haxhia 02 Ifil 20 Bridges 30 Hughes-Mason 34 Dawkin
Ref: Steve Martin