Portsmouth 0 Swansea City 2
Dyer was put through by a fine pass from Darren Pratley after Portsmouth captain Sol Campbell had been pulled out of position.
The tiny winger made no mistake as he lashed the ball home in the 26th minute.
The game had started brightly for Portsmouth with Armand Traore stinging the gloves of goalkeeper Dimi Konstantopoulos who got down well to save.
But it was Swansea that made the breakthrough through Dyer and they always looked comfortable after that.
Portsmouth striker Peter Crouch missed the chance to equalise on the half-hour mark when his volley from Jermaine Pennant's cross flew over the bar with the goal gaping. They were made to pay in first-half stoppage time when Swansea were awarded a penalty.
Live-wire winger Garcia Jordi Gomez was bought down by Traore's clumsy challenge on the edge of the box. The referee had no hesitation in pointing to the spot.
Top scorer Jason Scotland made no mistake as he sent David James the wrong way by firing into the bottom left-hand corner of the net to double the Swans' advantage.
Pompey came out firing after the break and Crouch again went close from Pennant's cross, with Konstantopoulos forced to produce a finger-tip save from his header as he pushed the ball wide by the left-hand post.
Barely three minutes later Swansea missed a glorious chance to seal the game through Gomez.
The midfielder was sent free in the penalty area by Pratley's fine ball but England goalkeeper James rushed out to block a certain goal by spreading himself in front of the chipped effort.
Portsmouth had accepted their fate by this point as last year's FA Cup winners went out to Championship opposition.