Boro, who have dropped into the relegation zone after a dismal run in the Premier League, take on Pep Guardiola's Manchester City in the FA Cup on Saturday.
The hosts fluffed numerous chances in the game and were made to pay for their profligacy in front of their faithfuls at the Riverside stadium.
The second half began in much the same way with Silva nearly scoring an identical goal to his opener but this one flew over the bar before Guzan managed to deflect an Aguero shot onto the post when City looked nearly certain to double their lead.
Silva opened the scoring sheet for Man City in the third minute following some sloppy defence from the home side.
Winning the Champions League with Manchester City would be the "biggest achievement" of Pep Guardiola's career if he succeeds, according to Yaya Toure.
Manchester City are unbeaten in their last nine games in all competitions to land Guardiola the prize as the best boss in the top flight last month.
The last time they conceded away from the Etihad was way back in January and that's sure to fill the team with massive confidence ahead of Wednesday's fixture. Two of the ties are all-Premier League bouts. "Go there and try to win the game".
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We had to continue to believe and stay together and I thought the goal encapsulated that and I couldn't be prouder of them. I want to thank the fans and players again because they have been fantastic for me".
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"Being a manager depends on results but I always believe deep in my heart that results depend on the way you play".
The former Ivory Coast worldwide believes that if his Spanish boss is able to deliver the UEFA Champions League to the club this season, it would go down as the biggest accolade in his managerial career. But it is starting to feel like something big is happening at City.
The midfielder's contract is set to expire at the end of the season, and no new terms have been agreed to keep him at Manchester City beyond this year.
"Normally that just happens in the final, but here it is in the semi-final too and of course we are so happy to be there, so happy".
But City are still alive in the FA Cup and Champions League and, even though Guardiola is prioritising team improvement, he realises the importance of silverware as a yardstick.
"As a coach I can be proud of my players".