Hereford ended their eight-game winless run with victory over Carlisle.
Two great saves from Hereford keeper Darren Randolph kept Carlisle at bay as he denied Danny Graham before diving to keep out Danny Livesey's header.
Williams lashed the ball into the net in the 60th minute to put Hereford ahead and was later denied a second when Ben Alnwick turned his shot away.
Things finally got worse for Carlise when defender Richard Keogh was sent off for elbowing Steve Guinan.
Hereford manager Graham Turner told BBC Hereford and Worcester:
"[In the] second half we played a bit more, opened them up and I was disappointed we didn't get a second, which meant we could have enjoyed more of the game.
"We did extremely well and I am delighted for the players, four points from two games is great for us, after conceding four goals at Oldham it was vital to keep two clean sheets.
"We got that shape we had at Brighton, we were slightly different at home where you need to push on, suddenly we played with a bit more freedom and created more chances.
"Once the goal went in you could see that bit of confidence come back.
"Providing we keep working and carry on doing what we've done in the last two matches and stay solid at the back there's every chance of climbing out of trouble.
"When you are bottom it's embarrassing, irrespective of the fact that we have just been promoted, so let's hope we can kick on from here."
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