The 28-year-old, the twin brother of England and Everton defender Michael, represented England up to under-20 level but declared his intention to play for the Republic in February 2019.
He qualifies for Ireland through his father and, with Steven Kenny's side desperate for goals, Keane has now been given his chance.
There is no place, though, for in-form Lincoln forward Anthony Scully, who has scored 10 goals this season.
Sheffield United full-back Enda Stevens, Derby midfielder Jason Knight and Rotherham winger Chiedozie Ogbene all return to the squad after injury ruled them out of September's international fixtures.
Captain Seamus Coleman and defender Dara O'Shea, though, are both ruled out through injury.
Teenage Norwich defender Andrew Omobamidele, who made his debut against Portugal, keeps his place but keeper Darren Randolph is left out again.
The Republic, who have picked up only two points from their five qualifying matches so far, take on Azerbaijan in Baku on October 9 before meeting Qatar three days later in Dublin.