Dane Gagai converted, but only after Jared Warea-Hargreaves was given 10 minutes in the sin-bin for dissent.
Roberts was in again three minutes later when Willie Mason burst into the clear, recovered from a failed tackle and offloaded.
Gagai, though, missed an easy attempt at goal to leave the door open for the fifth-placed Roosters.
Nuuausala took advantage to score a lucky four-pointer with less than 10 minutes to go, Sonny Bill Williams offloading close to the ground and Nuuausala inadvertently kicked it through and regathered to score.
James Maloney added the extras to put the visitors back in front before Roberts and Leilua responded.
In the first half, a penalty for a Willie Mason high shot put the Roosters in position early and they capitalised in the second minute when 18-year-old Sione Mata'utia made a horror start to his NRL career.
The fullback, on debut in place of Darius Boyd who is seeking treatment for depression, slipped over attempting to gather a Jake Friend grubber to gift Anthony Minichiello a try in the second minute.
The Roosters dominated the rest of the half, getting over the line three times but having no success against a scrambling defence.
Mata'utia gained some redemption for his early howler with a desperate chase to force a knock-on from Maloney in the 15th minute after the pair sprinted to a deflected Gagai kick.
The video referee's decision to overturn the onfield try was puzzling, while desperate defence from Robbie Rochow denied Maloney soon after.
Knights coach Wayne Bennett said it was his side's best win in a season of missed opportunities.
He said he could not prouder of their efforts given last week's poor performance in a 22-8 loss to Gold Coast in the Rise for Alex round.
Bennett praised the efforts of Roberts who he said had benefited from time at dummy-half in recent weeks when Kurt Gidley was at halfback.
"I said to him the other day I think this stint at halfback-hooker helped him just get a lot more confidence about him," Bennett said.
"I noticed it at training. I really thought tonight was going to be his night and he proved it. All the indicators were there."
Roosters coach Trent Robinson said his side failed to take their opportunities and were "out-scrapped in the end".
But he saved most of his criticism for the referees, saying it was a poor effort from the officials which "irked" him.
He pointed to a held-up decision against Maloney, the sin-binning of Warea-Hargreaves for swearing, the call to let Mason continue on after a tackle before the Knights' second try and Sione Mata'utia taking the ball dead and not conceding a line dropout.
"You could just feel it - the refs were looking for stuff from us," Robinson said.
- AAP
