Barmby missed the World Cup finals after being forced out by injury, but he still has ambitions to renew his England career and served notice that he is ready, willing and able to do so.
Barmby spoiled Manchester City's return to the Premiership, scoring a classic poacher's goal after only 15 minutes and setting up Leeds' second for Mark Viduka with a perfectly-weighted pass on the stroke of half time.
Barmby showed lightning reactions on the corner of the six-yard box to turn in Lee Bowyer's looping cross from the right and his long ball out of defence was perfectly judged for Viduka to run through and curl the ball round Carlo Nash.
To complete Terry Venables' joy, Robbie Keane netted Leeds' third goal with a brilliantly judged chip over Nash in the 78th minute, just eight minutes after replacing Viduka.
Eriksson was an interested spectator and he must have been impressed, not only by Barmby's goalscoring and goal-making exploits, but also his hunger for work on attack and defence.
The appointment of Venables and his subsequent signing of Barmby for £2.75million from Liverpool was not universally popular with Leeds fans but the doubters were quickly won over and when Barmby was substituted 12 minutes from the end he left the field to rapturous applause.
City, who stormed to the First Division title last season, not surprisingly looked attractive and vibrant going forward but their suspect defence suggests they could concede too many goals to Premiership attacks.
Nicolas Anelka couldn't mark his debut with a goal, squandering a good chance when Bowyer's backpass bounced off Paul Robinson's upper body and straight to him.