Viduka, who injured his back against Birmingham last December, exploited City's obvious shortcomings and obtained his first goals since he was twice on the mark against Manchester City on December 6.
It was a win carved out by a highly proficient performance that got Middlesbrough back up to speed after collecting only one point from their two opening games.
They completed a highly successful performance with a third goal from Frank Queudrue which only compounded a disjointed Birmingham display.
Poor Birmingham were simply off the pace and their recent additions have done little to improve their prospects, looking at their form in the first three games which have contained two successive home defeats.
Following the disappointment of their home reverse at the hands of Manchester City on Saturday, Birmingham, still without Emile Heskey, drafted in on-loan Jiri Jarosik who took the place of his former Stamford Bridge colleague, Mikael Forssell.
The front line, however, still lacked real penetration and the only real threat in the early stages came from a glancing header by Nicky Butt from a left-wing cross by Stan Lazaridis.
Birmingham had a let-off in the tenth minute when Jimmy Hasselbaink collected a pass from Queudrue but shot wide when clear. This, however, indicated the problems facing Birmingham so early in the season.
There was a little more determination from the North East side as they demonstrated in the 14th minute when James Morrison produced a low cross from the right into the path of Viduka for the Australian to score with an angled left-foot shot.
Viduka should have added to his tally four minutes later when Maik Taylor's clearance went straight to the Boro striker who took far too long to make up his mind to shoot and as a result Matthew Upson was able to race back 20 yards to block the delayed shot.
It was a terrible miss and allowed struggling Birmingham to remain in contention despite their shortcomings in midfield and up front.
But Viduka didn't allow this miss to put him off his game. The former Leeds man demonstrated his class with a superb second goal in the 44th minute.
He collected a Queudrue throw-in near the bye-line, turned inside two Birmingham defenders and lashed a stunning shot high into the far corner of the net from an almost impossible angle.
The former Aston Villa central defensive due, Gareth Southgate and Ugo Ehiogu resumed their partnership and, as usual, rarely put a foot wrong.
It was the industry of another former Villa man, George Boateng, which was significant on the night as he relentlessly maintained a high level of competition to the frustration of the Birmingham side.
Manager Steve Bruce drafted in Forssell and Muzzy Izzet for Olivier Tebily and Stephen Clemence but Middlesbrough were clearly determined to defend their first half advantage.
As a result there was an air of frustration about Birmingham despite enjoying most of the attacking play. They suffered a further set-back when Queudrue appeared on the blind side to convert Stuart Downing's 71st minute free-kick.