The 22-year-old midfielder was best placed to tuck home Christian Schwegler's cross midway through the second half, keeping Salzburg three points clear of Esbjerg in the race to top the standings.
They look certain to do so unless the Danes, who beat Standard Liege 2-1 on Thursday night, can pull off a free-scoring win at the Red Bull Arena in two weeks' time.
It was, however, a fourth defeat in five for Sweden's Elfsborg, who visit Liege on matchday six with a view to possibly snatching third spot from the Belgians and taking the edge off a poor campaign.
To the casual observer it would clearly become apparent which side had been comfortable in the group and which one had floundered, as Salzburg dominated from the first whistle.
Stefan Ilsanker tested Kevin Stuhr-Ellegaard's reflexes with an early sighter from distance and Florian Klein blasted over the Elfsborg bar in the 22nd minute.
The opening goal arrived six minutes before half-time as Schwegler delivered the ball into the box from the right, and it was quickly dispatched by the lurking Meilinger.
Elfsborg appeared to wake up slightly as the break approached but Niklas Hult could only screw his finish over Peter Gulasci's crossbar.
Although the hosts managed to better close ranks in the second half, there was little to cheer for fans of either team, who sat through 45 dull minutes which bore only two shots on goal.
When the first arrived it caused home goalkeeper Abbas Hassan - a half-time replacement for Stuhr-Ellegaard - plenty of problems as he sprawled to parry Sadio Mane's effort to safety.
Havard Nielsen was the next, and last man, to try his luck but could not find the target as the ball whizzed past Hassan's goalmouth before the game fizzled out to its scrappy conclusion.