Silva’s side squandered chances to add to a 29th-minute opener from debutant Harry Wilson, a £12million signing from Liverpool.
However, as so often last season, when Fulham were relegated from the Premier League, they were unable to convert their attacking play into goals, and Marc Bola punished them 13 minutes from time with Boro’s equaliser.
The season started with a bang as Aleksandar Mitrovic was shown a yellow card for his first challenge, a shoulder-charge into the head of Boro captain Jonny Howson.
New Fulham goalkeeper Paulo Gazzaniga had an unsteady start, almost caught out of his ground by Antonee Robinson’s backpass, then missing his punch from Paddy McNair’s corner.
But Fulham looked good further forward. Josh Onomah forced a corner after two exchanges of passes with Wilson and a fortunate deflection took a shot from Fabio Carvalho into the arms of Joe Lumley. Wilson’s powerful volley then drew a leaping save from goalkeeper Lumley.
Tempers flared on the touchline and both assistant managers, Fulham’s Luis Boa Morte of Fulham and Middlesbrough’s Kevin Blackwell, were shown yellow cards by referee Keith Stroud after an altercation.
But just before the half-hour all attention was back on the football as Fulham went ahead.
Wilson took a short pass from Onomah on the right, cut inside past Bola and hit a low hard shot with his left foot that passed between the feet of defender Dael Fry on its way into the corner of the net.
Boro’s Uche Ikpeazu was then fortunate to escape with a yellow card after leading with his forearm as he challenged for a bouncing ball with Fulham captain Tim Ream.
The hosts opened the second half in lively fashion but loud appeals for a penalty when Carvalho fell under challenge from Sam Morsy went unheeded by Stroud. Carvalho then shot wildly after Mitrovic had opened the Boro defence with a headed flick.
The Cottagers should have doubled their lead after 63 minutes but Neeskens Cabano headed straight at Lumley from Kenny Tete’s cross – and Boro survived another near miss five minutes later when Lumley missed Cabano’s cross but Wilson could not take advantage.
And Fulham paid for their wastefulness after 77 minutes when Bola took a pass from substitute Isaiah Jones and hit a low angled shot across Gazzaniga and inside the far post for his second league goal for the club.
Another substitute, Marcus Tavernier, had the chance to steal all three points for the visitors – but he blazed his shot high and wide.