“GREAT PERFORMANCES Lady Gaga and Tony Bennett”: Lady Gaga and Tony Bennett perform. (Courtesy of Joseph Sinnott/Courtesy of Joseph Sinnott)

Emotions run high in Morocco when the contestants start to think that some racers are playing dirty on “The Amazing Race” (CBS at 8 p.m.).

Mike and Chuck debate a proposed school merger while Boyd takes advantage of his mom’s profession and dresses up as a piece of coal for Halloween on “Last Man Standing” (ABC at 8).

RETURNING SHOW: “Grimm” (NBC at 9) opens Season 4 with Nick mourning the loss of his Grimm powers while the town braces for a new enemy.

For the strangest moment on television tonight, tune in to “Great Performances: Tony Bennett and Lady Gaga — Cheek to Cheek Live!” (MPT at 9 and WETA at 9:30). The pair will perform songs from their collaborative classic-jazz album. The costume possibilities are endless.

The fans have spoken and voted, and one booted model comes back to the house on “America’s Next Top Model” (CW at 9).

“Mysteries at the Museum” (Travel at 9) looks into the stories behind a Boy Scout badge that inspired a teen’s nuclear experiment and a chess set used in the “Match of the Century,” the 1972 tournament between American Bobby Fischer and the Soviet Union’s Boris Spassky.

The documentary “Leave the World Behind: Swedish House Mafia’s Final Tour” (Showtime at 9) zooms in on the breakup and farewell tour of the electronic dance supergroup.

SERIES PREMIERE: Based on the “Hellblazer” comic books (and the Keanu Reeves movie), “Constantine” (NBC at 10), which is reviewed by Post TV critic Hank Stuever on Page C1, follows demon hunter John Constantine (Matt Ryan), whose soul has been condemned to hell, back into his fight against the spawn of Satan.

“Real Time With Bill Maher” (HBO at 10) hosts journalist James Risen, climate activist Chloe Maxmin, political commentator John Avlon, political consultant Mary Matalin and activist Cornel West.

RETURNING SHOW: Garry Trudeau’s “Alpha House” (Amazon), which stars John Goodman, returns for a second season just in time for the midterm elections.

“Homeland” actress Claire Danes and Little League superstar Mo’ne Davis are on “The Tonight Show Starring Jimmy Fallon” (NBC at 11:35), with music from Fences featuring Macklemore.

Comedian Jerry Seinfeld is on the “Late Show With David Letterman” (CBS at 11:35), along with a sampling from Cirque du Soleil’s “Michael Jackson One.”

Rachel Lubitz