Rangers extended their unbeaten run to six matches after being held to a 0-0 draw by Kilmarnock at Rugby Park.
The visitors were denied by a string of impressive saves by Freddie Woodman in a result which leaves them 12 points behind second-placed Aberdeen while Killie stay seventh.
Kilmarnock started well with Gary Dicker's header from a Jordan Jones free-kick saved by Wes Foderingham, while Tavernier headed over the bar following a corner.
The visitors, who handed senior debuts to defenders David Bates and Myles Beerman, dominated as the half wore on with Conor Sammon firing a shot over the bar from a tight angle while Woodman produced fine saves to keep out Joe Garner's header and Emerson Hyndman's low drive.
Pedro Caixinha's side continued to carve out the better opportunities in the second half with Garner's header hitting Martyn Waghorn's knee and being pushed wide by the keeper.
Garner continued to be in the thick of the action and forced Woodman into another good save with a header while the visitors had a penalty appeal turned down minutes later after a cross appeared to cannon off Salmon's arm.
Woodman denied Rangers again when he kept out Waghorn's effort from inside the area after the striker had won the ball on the right flank.
Joe Dodoo and Josh Windass were brought on in the closing stages but Lee McCulloch's men held on for a point to extend their unbeaten run to four matches.