Keane claimed his 47th and 48th goals for the national team as Wolverhampton Wanderers utility man Stephen Ward and West Bromwich Albion striker Simon Cox marked their debuts with their first international goals.
It proved to be a disappointing night overall for Northern Ireland, who were cheered on by a sparse band of supporters after fans staged a boycott in protest at travelling restrictions placed upon them.
Ward opened after 24 minutes and Keane doubled for the hosts following a poor pass-back by Lee Hodson eight minutes before the break.
There would be further misery for Northern Ireland when Craig Cathcart scored an own goal a minute before the interval.
The Republic of Ireland added to their tally nine minutes after the restart when Adam Thompson was deemed to have fouled Keane in the box and was given a straight red card by Scottish referee Craig Thomson. Keane stepped up to score from the penalty spot.
The victory put the Republic of Ireland at the top of the Nations Cup table ahead of Scotland's game against Wales tomorrow.