Robson opened the scoring after just 22 seconds and both sides struck the woodwork before former Royals striker Leroy Lita added a second for the Teessiders in the 41st minute.
Jimmy Kebe's superb solo effort dragged Reading back into the game prior to the interval, but David Wheater restored the hosts' two-goal advantage with a header from Robson's 68th-minute corner.
Reading's misery was compounded late on as Brian Howard received a straight red card for a foul on Middlesbrough substitute Andy Halliday.
The result lifts Boro above the Royals in the npower Championship table and manager Gordon Strachan will take great heart from a much-improved showing in which his side finally displayed their promotion credentials.
Tarmo Kink was recalled to the Boro side after coming off the bench to score both of his side's goals in Tuesday's 2-1 win over Burnley.
Nicky Bailey and Wheater also returned, with Gary O'Neil and Matthew Bates missing out and Halliday dropping to the bench.
Brynjar Gunnarsson replaced Simon Church in the only alteration to the Reading side that drew 0-0 at Millwall.
Boro made a stunning start and took the lead when Robson latched on to a neat through-ball from Bailey and broke clear before cracking a powerful left-footed shot into the far corner.
Reading struggled to respond and were grateful to Adam Federici as the goalkeeper denied Lita on two occasions before keeping out another firm strike from Robson.
Reading had a lucky escape in the 22nd minute when Scott McDonald volleyed against the bar following an error by Matt Mills.
The Royals were then denied by the woodwork themselves as Kebe directed a shot onto the post from Jobi McAnuff's cross.
Kink and Bailey fired over as Boro continued to enjoy the better of proceedings.
And the hosts added a second goal four minutes before the interval when Lita beat the offside trap before squeezing a shot past Federici.
The Royals were handed a lifeline in the 44th minute courtesy of a stunning individual strike from Kebe, who exchanged passes with Howard and waltzed past several challenges before side-footing home.
Reading then saw appeals for a penalty rejected after Julio Arca appeared to barge Shane Long to the ground.
Kink wasted a glorious chance to grab a third for Boro eight minutes after the interval, the Estonian dragging his shot wide after being put through one-on-one.
A deflected effort from the lively Lita flew narrowly wide as the Teessiders piled on the pressure once again.
Gunnarsson blocked a Wheater strike from the resulting corner, before Harte went close at the other end with a thunderous strike that ricocheted off a Boro defender.
Reading's hopes of rescuing something from the game then suffered a hammer blow as Wheater rose highest to convert Robson's inswinging corner from the right.
The visitors huffed and puffed in search of a second goal, but were unable to seriously test Boro keeper Jason Steele.
A miserable afternoon for Reading was rounded off when Howard saw red after appearing to go over the ball in a challenge with Halliday.