Goals from Ryan Taylor and Jed Wallace secured Awford his first win since taking charge following Richie Barker's sacking on Thursday. Newport defender Ismail Yakubu scored a second-half header for the home side, who had midfielder Adam Chapman sent off in the first half before Darcy Blake was also dismissed in the second period.
The win moves Portsmouth five points clear of the League Two relegation places.
Taylor gave Portsmouth the lead with a penalty in the 22nd minute after he had his shirt pulled in the box by Kevin Feely. Chapman was then sent off shortly afterwards for a reckless two-footed lunge on Danny Hollands near the halfway line.
Wallace doubled Portsmouth's advantage before the break with a firm header from Ricky Holmes' cross.
Yakubu gave Newport lifeline 16 minutes from time when he headed home Robbie Willmott's corner from six yards.
But despite plenty of late pressure from the home side, they couldn't find an equaliser and their cause was not aided when Blake accrued a second yellow card seven minutes from time.