But he couldn't have timed his strikes better as Boro tore into United after showing them too much respect and giving them too much time on the ball in the first 20 minutes.
Alves scored twice - his first cancelling out Cristiano Ronaldo's early opener - and then he put Boro ahead as the home team rocked United back on their heels.
Portuguese goal machine Ronaldo won't score an easier goal this season than his tenth minute strike.
The Boro defence failed to clear a United corner and then compounded their mistake by gifting Michael Carrick too much time on the ball.
When he stabbed it into the middle, the unmarked Ronaldo couldn't miss from six yards.
Emanuel Pogatetz and Alves both went close, but it was United who looked the most likely to score until Luke Young produced a superb block to deny Wayne Rooney.
When Boro stepped up a pace, Julio Arca produced a defence-splitting pass to set up Jeremie Aliadiere, but the Frenchman dragged his shot wide.
Ronaldo slalomed past four Boro defenders but blazed wide before Boro finally tested Edwin Van der Sar in the United goal.
A 35-yard free kick from Alves was only kept out by a combination of Van der Sar's arms and body.
But Boro weren't to be denied and were level on 35 minutes when Gary O'Neil's lob forward was headed on by Aliadiere and Alves drilled the ball home.
Boro almost went into the break ahead but Van der Sar produced an acrobatic save to deny Stewart Downing, who was left unmarked at the far post.
United appealed loudly for a penalty when Andrew Taylor went to ground to block Ronaldo's shot but referee Mike Riley waived play on.
The roof almost came off the Riverside Stadium when Alves calmly struck his second goal on 56 minutes.
The Brazilian pounced on a poor clearance by Wes Brown and then held off Rio Ferdinand's challenge to curl the ball sweetly past Van der Sar.
Three minutes later, Alves almost grabbed a hat-trick but he was blocked by Ferdinand.
In a pulsating finish, United grabbed an equaliser when substitute Ji-Sung Park tricked his way past Taylor and pulled the ball back for Rooney, whose shot deflected off the immaculate David Wheater and into the back of the net.
It was disappointing for Boro who matched the champions every step of the way and in stoppage time they almost grabbed the winner but Sanli Tuncay was denied by Van der Sar.