Denmark secured their first-leg win at home with a 2-1 win at home to Wales, their best goal being Gareth Bale in the 90th minute.
With just one point behind them, the Danes now have seven points in Group 4, one more than Wales, who will not play again, while Ireland have only one point and is already relegated.
Also in the second tier, Ukraine, who had already secured a place in the top flight, lost their first points in their last Group A encounter when they lost 4-1 at home to Slovakia.
The Ukrainians end the group with nine points, with Slovakia and the Czech Republic, both with three points to discuss in the last round maintenance.
All were equal in Group C of League C with draws to a goal between Cyprus and Bulgaria and between Norway and Slovenia, with Norwegians and Bulgarians leading with 10 points, six more than five than Cypriots and nine than Slovenes.
In Group D of the League D, the favoritism was confirmed, with Armenia thrashing Gibraltar 6-2 and Macedonia winning 2-0 at Liechtenstein.