Bobrovsky made 33 saves and the Blue Jackets defeated the Tampa Bay Lightning 3-1 at Amalie Arena.
Bobrovsky made 52 saves in a 4-3 shootoot win against the Panthers on Thursday.
"It was a good challenge for us," Savard told the Blue Jackets website. "Obviously they're a huge team with good offensive weapons too. But I think everyone did the job tonight."
Columbus (9-15-2) controlled play early in the Lightning zone and scored on its third shot, 2:37 into the period. Blue Jackets forward Matt Calvert passed to Jenner, whose wrist shot from the left circle beat goalie Ben Bishop short-side for his fourth goal.
"To go on the road and sweep a road trip, it's a great feeling," defenseman Jack Johnson said.
Columbus, which went 1-for-4 with the man advantage, converted on its first power play when Jack Johnson passed to Savard, who sent a wrist shot from inside the right circle on goal and it trickled past Bishop at 12:48.
Bishop kept it a one-goal game with several big saves in the period, including one against Skille, who faked a pass, causing Lightning defenseman Radko Gudas to slide. Skille's shot hit Bishop in the chest. Bishop had won his past five games.
The Blue Jackets had a breakaway chance later in the period after a turnover by Lightning forward Nikita Kucherov went right to Brian Gibbons' stick. Gibbons deked before his shot hit Bishop's pads and flipped over the net.
"This was a big test for us," Skille said. "We needed a strong push for all three periods and I think we did that."
Columbus led 2-0 after the first period despite being outshot 14-9. Bobrovsky made a point-blank save on Brenden Morrow with 2:17 left in the first period to maintain the two-goal lead.
"We didn't deserve the points," forward Steven Stamkos told the Lightning website. "You've got to give them credit. Their goaltender played well and their team played well."
During a 4-on-4 situation and less than two minutes remaining in the second period, Lightning defenseman Anton Stralman sent a pass through the crease but Ondrej Palat was unable to put the puck in a vacant net with Bobrovsky out of position.
Skille made it 3-0 off a rush after he came out of the penalty box 4:51 into the third period. Scott Hartnell cleared the puck from the Columbus zone off of the boards to Michael Chaput, who fed Skille in a 2-on-1. Skille's pass to Calvert was deflected by Kucherov past Bishop.
"It was just one of those nights, the bounces didn't go our way," Bishop said. "We had a couple of bounces off of our own player and pucks were bouncing over our sticks. Every now and then, that's going to happen."
Palat scored the Lightning's lone goal on a tic-tac toe passing play from Kucherov and Tyler Johnson at 18:47 of the third period during a 4-on-4 situation and Bishop pulled for an extra attacker.
It was the fourth regulation loss for the Lightning (18-7-3) in their past 19 games. Tampa Bay fell to 11-3-1 at home.
"They got the lead and shut it down," Lightning coach Jon Cooper said. "They played a good road game."