Rangers extended their unbeaten Scottish Premiership start to nine matches with a convincing 5-1 win at Motherwell which keeps them top.
George Edmundson's late own goal was little consolation for the home side.
Tavernier's opening spot-kick was Rangers' first in the Premiership in 11 months, while Motherwell have now given away nine penalties in 12 games this season.
Celtic remain one point behind their Glasgow rivals with a game in hand after cruising to a 3-0 home win against Hibernian.
First-half goals from Callum McGregor and Albian Ajeti gave Celtic a 2-0 half-time lead and Mohamed Elyounoussi added a third with 11 minutes remaining.
Neil Lennon's side also remain unbeaten in the Scottish Premiership and have dropped only two points from their first eight matches.
Hibs, without a win at Celtic Park since January 2010, remain third in the table.
They were punished after wasting several chances, with Christian Doidge, Kevin Nisbet and Joe Newell all missing the target from in front of goal.
Aberdeen closed to within two points of Hibs after easing to a 3-0 win at 10-man Ross County.
Lewis Ferguson converted two second-half penalties after Marley Watkins' header had given Aberdeen a 1-0 lead at the interval.
Ferguson scored his first from the spot after County skipper Iain Vigurs had been sent off for his trip on Ross McCrorie and struck again from 12 yards after Josh Reid had been penalised for handball.
County have lost three of their last four league games and are seventh in the table, four points above the bottom two.