Saturday's sold-out Aviva Stadium clash marked the start of new eras for both teams as Heimir Hallgrimsson led the hosts against a nation beginning life after Gareth Southgate.
England impressed in their first match since losing July's Euro 2024 final, with Rice and Grealish setting Carsley on course for an impressive win over the nation he played for 40 times.
Rice and Grealish were targeted by protesting home fans, with one banner having pictures of them alongside the words, "The snakes are back."
Both players, and their manager, were born in England.
Rice won three senior caps for the Republic and fired England into an early lead, which former Ireland U21 international Grealish added to during a one-sided first half.
"We both enjoyed our time playing here. I certainly did," Grealish said.
"I have a lot of Irish in my family, so there's no bad blood whatsoever from my side."
Julian Nagelsmann's Germany side opened their campaign with an emphatic 5-0 win over Hungary in Dusseldorf.
Niclas Fullkrug opened the scoring before the break, with Jamal Musiala, Florian Wirtz, Aleksandar Pavlovic and Kai Havertz all getting on the scoresheet as the visitors wilted in the second half.
"That was fun. We're very happy to have them (Musiala and Wirtz) at this level in our group," Fullkrug said.
"It's a gift that will bring a lot fun to all German spectators in the upcoming years."
Five goals from as many men lifted the Netherlands to a 5-2 triumph over Bosnia and Herzegovina in the evening's other A3 clash.
Joshua Zirkzee heads home one of five Dutch goals against Bosnia and Herzegovina. (AP PHOTO)
Manchester United summer signing Joshua Zirkzee scored in the 13th minute at PSV Eindhoven's Philips Stadion but saw his opener cancelled out by Ermedin Demirovic 14 minutes later.
Tijjani Reijnders restored the hosts' lead in the second minute of first-half added time before Liverpool's Cody Gakpo netted 11 minutes after the restart.
Edin Dzeko clawed one back in the 73rd minute, but the Dutch had more to come as Wout Weghorst made it four in the 88th minute and Xavi Simons added his name to the scoresheet in the 92nd.
Elsewhere, a Fotis Ioannidis brace and Benjamin Kallman's own goal secured England's group B2 rivals Greece a 3-0 victory over Finland.
Georgia came out on top of their B1 opener with a comfortable 4-1 victory over the Czech Republic, while Albania beat Ukraine 2-1 in the group's other encounter.
Faroe Islands and North Macedonia drew 1-1, while Armenia opened their campaign with a 4-1 victory over Latvia, also in C4.
Moldova beat Malta 2-0 to kick-off their D2 campaign.
With AP & DPA.
