After spurning a number of chances, United took until the 87th minute to score as Williams broke down the left and then jinked inside before firing into the top corner.
United had the opportunity to go in front towards the end of a relentless first half but captain Katie Zelem’s 40th-minute penalty was saved by Reading goalkeeper Jacqueline Burns after Alessia Russo was brought down by Diane Caldwell.
Burns made a string of impressive saves, twice denying Lucia Garcia in one-on-one situations, while United winger Nikita Parris hit the crossbar late in the first period.
But despite having to withstand sustained pressure from the visitors, Reading did have chances of their own and looked set to secure a valuable point.
However, United’s pressure finally told late on – and after Chelsea’s match against Liverpool earlier in the day was postponed because of a frozen pitch, the win puts Marc Skinner’s team top of the league on goal difference.
“I still don’t think we’re anyway near the evolution of what we want to achieve here,” Skinner told BBC Radio Manchester.
“But we’re exciting. We’re pushing and we’re going to keep pushing for every game that the season gives us to be challenging for a title.”
Persistence pays off for Man Utd
While they fought hard, there were times when Kelly Chambers’ side simply could not cope with the pace and precision of United’s play.
However, the finishing was not so clinical and before Williams’ intervention, it was beginning to look as though they would have to settle for a point.
Burns was called into action six times during a breathless first half and it should have been more as Russo, Garcia, Parris and Ella Toone combined brilliantly to slice through the home defence.
Too often, though, the final pass or the finish was lacking. When it wasn’t, they found an inspired Burns in the way and on the occasions even she looked beaten, a blue and white shirt would appear to block the shot.
Reading were clinging on by their fingertips but were offering enough of a threat on the counter to keep United honest, especially as the game entered the last 15 minutes.
It took a smart save from Mary Earps to keep out Justine Vanhaevermaet’s glancing header but the scare did not quell the away side’s attacking intent.
They continued to pour forward, risking defeat in their pursuit of victory, and – eventually – they were rewarded.
“I’m gutted. We deserved something out of the game today,” Chambers told BBC Radio Berkshire.
“The way we conceded was really disappointing because you could see when we conceded that the girls just fell to their knees, they were gutted. For me, it’s a performance to be proud of but a result to be disappointed about.”
There is a long way to go in the race for the WSL title but if United do emerge victorious, as much as thumping wins like last weekend’s 6-0 thrashing of Liverpool, it is games like this that will have taken them there.
“Reading made it so difficult for us,” Skinner added.
“We knew it would be last 20 minutes but they made it so, so difficult for us. That is a better one for us because of the way we had to win it.”