A Christmas Day drive-by shooting has left a Staten Island minister and her son recovering from gunshot wounds — and cops searching for both motive and suspect.

The mom and son had just pulled their SUV away from the curb outside a deli on Jersey Street at 3:15 p.m. on Monday when another SUV pulled out from ahead of them and began tailing them, police sources told The Post.

After a couple of turns, the mom — Monique Hall, 42, a minister at the First Central Baptist Church on Wright Street — realized the SUV was following her and her son, Dayvon, 19, through the New Brighton neighborhood, the sources said.

Suddenly, at a stop sign at Highview Avenue and Filmore Street, the female driver stuck a gun out of the driver’s side window and began shooting.

Some seven shots rang out. The minister, who is also a member of her local Community Education Council, was shot in the lower back. Her son was shot in the left shoulder and grazed in the head.

Both have been released from Richmond University Medical Center.

Investigators believe the pair may have been unintended victims in a case of mistaken identity.