Celtic has an five-point lead over Rangers, but its Glasgow rival still has three games in hand.
Stokes set up a 44th-minute opener for Gary Hooper and netted himself from the penalty spot five minutes into the second half after being brought down by Lewis Stevenson.
Stokes, who moved to Celtic from Hibs in August, skillfully netted his second in the 65th, sending an overhead kick from Emilio Izaguirre's corner into the bottom corner.
"It was pretty comprehensive in the end and but for better finishing it could've been a few more," Celtic manager Neil Lennon said. "We were a bit sloppy in the first 20 minutes and I thought once (Beram) Kayal got a grip on the game for us, he got us playing. He got our strikers in the game."
At Ibrox, Vladimir Weiss netted from long range for Rangers in the 25th before winning a penalty two minutes later and Steven Whittaker scored from the spot.
Weiss was on target again in the first-half stoppage time, curling a free kick past Tomas Cerny after being fouled by Grant Gillespie.
Maurice Edu sealed the victory in the 82nd, with the United States midfielder collecting a throw in from Whittaker before cutting into the middle and scoring from 18 meters (yards).
"Weiss played very well. When the opposition are set out in that manner, sometimes it takes something a bit special and his first goal was excellent," Rangers manager Walter Smith said. "He then got the penalty and scored another goal so I am delighted for him. Consistency as much as anything else is probably the main thing for him now."
Kilmarnock is nine points behind third-place Hearts after conceding a late leveler to draw 1-1 with St. Johnstone, fifth-place Inverness was held to a 0-0 draw at Motherwell and Aberdeen is five points from the bottom after beating St. Mirren 2-0.
