Manly laid the foundations for their victory with three tries in the opening 20 minutes scored by Jamie Lyon, Williams and Matt Ballin.
The Dragons were the masters of their own downfall with some sloppy play in possession early in the game, but dominated for long spells after a maiden try on the stroke of halftime from Nathan Green.
The hosts came charging out of the blocks after halftime with Green scoring his second try before Michael Weyman returned from his injury lay-off in style by powering over from close range.
A Chase Stanley four-pointer levelled the scores in the 64th minute but Jamie Soward missed the chance to take the lead with a horrible conversion attempt that sailed wide to the right of the posts.
Manly took full advantage of that reprieve and with one of their few forays into Dragons territory, Taufua, who was put on report for a shoulder charge on Jason Nightingale, finished brilliantly to steal the points in a game where they had only 40 per cent of possession.
Stewart and Morris will undergo scans on Tuesday but both clubs said the injuries don't look too serious.
"I am not quite sure what happened to Brett, he said he copped a knee in the back, so at halftime we decided to leave him off as a precaution," Manly coach Geoff Toovey said.
"He seems alright in the sheds now but we'll wait to see what the scans say."
The Dragons' performance director Andrew Gray said he was confident Morris had not sustained any significant damage but would again have to wait and see.
"Brett just had a twisting injury to his knee and he seems to have a bit of a sprain on the outside of his knee," Gray said.
"But we need to scan him tomorrow just as a precaution to exclude the possibility of there being any other damage inside his knee, but at this stage it doesn't seem to be too serious."
Toovey was full of praise for his players for securing the win without the presence of injured Jason King and suspended pair Richie Fa'aoso and Steve Matai.
"It was a hard win for the boys, we defended very strongly for one another and it was a very pleasing to get the two points," he said.
Dragons coach Steve Price cut a frustrated figure and said the loss was hard to stomach after his side had dominated for long spells.
"When you dominate in possession and in metres and come away with a loss it's hard to take," he said.
- AAP