Silvera pounced in second-half stoppage time as Boro stretched their winning run to six successive matches, having failed to taste victory in their opening seven.
Norwich scored even later, with Jonathan Rowe grabbing his eighth of the season, but it was no more than a consolation in a 2-1 defeat for the hosts.
"I'm absolutely delighted for Sammy," Middlesbrough manager Michael Carrick said.
"We didn't have a lot of the ball and I thought there'd be space for Sammy to exploit with his sharpness and his cleverness."
Having struggled for regular game time at Boro, Silvera has twice featured for the Socceroos in recent friendlies, and made the most of his opportunity on Tuesday night.
"He's not had a lot of football over the last few weeks but he's a great lad and his character is fantastic," Carrick said.
"He's trained so hard, and I told him to be patient and that there'd be chances for him to make an impact.
"There's no bigger impact than coming on and scoring the winning goal."
Leicester edged out Sunderland 1-0 to record an eighth successive league victory that put them eight points clear at the top of the Championship as they look for an immediate return to the Premier League.
Massimo Luongo and Cam Burgess' second-placed Ipswich have two games in hand on the leaders, the first at Bristol City on Wednesday.
West Brom moved back into the top six with a 2-0 win over 10-man QPR.
It was a fifth straight defeat for QPR, who had arrived at The Hawthorns late to force a 10-minute delay to kick-off.
Cardiff are up to sixth after thrashing Huddersfield 4-0, ending a run in which they had taken only one point from three games.
Blackburn sit just one point off the play-off places after Callum Brittain's first goal for the club helped them to a 2-1 win over managerless Millwall at The Den.
Ken Sema's first goal of the season was enough for Watford to beat Swansea 1-0.
Sema hit a powerful shot eight minutes from time to lift the Hornets away from the relegation zone.
- with PA
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