Alli, 19, has made just three Premier League starts but has been included amid injuries to regular central midfielders Jordan Henderson and Jack Wilshere.
Ings has been rewarded for scoring two goals in three games for his new club and benefits from the absence of team-mate Daniel Sturridge, who has just returned from injury.
England have already qualified for next summer’s European Championships and won all eight group games ahead of next week’s visit from Estonia and a trip to Lithuania days later.
“The game in Lithuania is the one where, if any experimentation takes place, it’ll be there,” said Hodgson. “It may damage our chances of getting the perfect 10 but I’m prepared to accept that.”
Hodgson admitted Alli’s selection was “offbeat” but called the former MK Dons player “a very exciting talent”. He added: “He’s so young and has only just broken into the Tottenham team, but we’re very impressed with what we’ve seen.”
Full England squad
Goalkeepers: Jack Butland, Joe Hart, Tom Heaton.
Defenders: Ryan Bertrand, Gary Cahill, Nathaniel Clyne, Kieran Gibbs, Phil Jagielka, Phil Jones, Chris Smalling, John Stones.
Midfielders: Dele Alli, Ross Barkley, Michael Carrick, Adam Lallana, James Milner, Alex Oxlade-Chamberlain, Jonjo Shelvey.
Forwards: Raheem Sterling, Danny Ings, Harry Kane, Wayne Rooney, Jamie Vardy, Theo Walcott.