The West Ham United duo again partnered one another in central midfield as the Boys in Green made it ten points out of 12 with a comfortable victory at Dublin’s Tallaght Stadium.
Queens Park Rangers striker Reece Grego-Cox helped himself to a hat-trick, with Everton midfielder Harry Charsley also on target.
Ireland kicked-off their challenge for a place in next summer’s finals in Italy and San Marino with a 1-0 win over Kosovo and 3-1 victory in Azerbaijan – Rice’s U21 debut – before holding Norway to a goalless draw in Dublin last Thursday evening.
The Irish will end the current international break top of Group 5, but could see their lead cut to a single point when second-place Germany travel to Norway on Tuesday evening.
Rice and Cullen return to international action on 14 November, when they travel to Norway.
Elsewhere, former West Ham youngster Sean Maguire, who joined Preston North End following a prolific two-year spell at Cork City, made his full debut for Ireland as a late substitute in the 2-0 FIFA World Cup qualifying Group D win at the Aviva Stadium on Friday evening.