Two goals from Gareth McAuley and a third from Kyle Lafferty sealed the victory while there was more good news for the Irish from Budapest where rivals Hungary and Romania played out a goalless draw.
Joan Edmundsson had briefly hit the visitor's hopes with a 36th-minute equaliser but he was later sent off and Michael O'Neill's men now go into next Tueday's (AEST) Belfast clash with the Hungarians knowing qualification is within their grasp.
Romania dropped to second after its Budapest stalemate but will be happier with a point which maintains its three-point gap over the third-placed host with three relatively favourable group games remaining.
Finland piled more misery on 2004 champion Greece with a 1-0 win in Piraeus which leaves the Greeks bottom of the group and still without a win with two points from its seven games played so far.
Germany clambered to the top of Group D with a 3-1 win over Poland in Frankfurt.
Thomas Muller's opener and a brace from Mario Gotze sunk the Poles, who had briefly reduced the deficit through Robert Lewandowski's strike towards the end of the first half.
The win puts Germany two points clear of the second-placed Poles, whose first defeat of the campaign leaves it looking anxiously over its shoulders in a bid to avoid sinking into a play-off place.
Scotland's shock 1-0 defeat in Georgia handed the initiative to the Republic of Ireland in the race to secure at least a third-place finish.
The Scots had started the night with their eyes still on an automatic qualification slot but their hopes were shattered after Valeri Kazaishvili's match-winning strike towards the end of the first half in Tbilisi.
Republic of Ireland was in no mood to let its opportunity slip by and moved above the Scots into third place with two goals from Robbie Keane and one each for Cyrus Christie and Shane Long securing a 4-0 win over Gibraltar.
And Gordon Strachan's men must be left hoping for more heroics from the Georgians when they visit Dublin to face Ireland on Tuesday (AEST).
In Group I Denmark failed to make the most of home advantage as it was held to a goalless draw by Albania in Copenhagen.
The result leaves the Albanians level on points with the Danes with a game in hand, a further point behind group leader Portugal.
Already-eliminated Serbia sealed a 2-0 win over Armenia in Novi Sad with an own goal from Levon Hayrapetyan and a second-half strike from Adam Ljajic.
