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Roglic, who finished ninth in Stage 1 as his Jumbo-Visma team-mate Wout van Aert took the win, now moves to the top of the General Classification as his team's superb start to the event continued.
With 12km left of the stage, Team Ineos hit the front, taking the lead from Bruno Armirail (Groupama-FDJ) ahead of the final climb.
Roglic and Thomas Dumoulin responded to a late charge from Emanuel Buchmann (Bora-Hansgrohe) and Pavel Sivakov (Team Ineos) and found themselves in front.
It was Roglic who maintained his challenge and saw off moves from Buchmann and Nairo Quintana (Team Arkea-Samsic) to seal the win.
"It's a great result for our team," Roglic said after the finish.
"Once again we show that we prepared right. The whole team did a really great job and I'm happy to finish on top again.
Critérium du Dauphiné Stage 2 Highlights - Primoz Roglic blows Ineos away as Thomas and Froome crack
"We all knew about the hard climb at the finish and we started to control the race from the beginning. The guys are really strong so they managed it perfectly and in the end, I was happy to be able to win this.
"Egan [Bernal] is the Tour de France winner so he’s the strongest, or one of the strongest. But everyone is very prepared and you have to be the best in the end. It was quite a strange season. I’m happy with every race I can do this year and I’m really happy with the way it’s going."
CRITERIUM DU DAUPHINE STAGE 2 TOP 10
1 Primoz Roglic (Slo) Team Jumbo-Visma 3:39:40
2 Thibaut Pinot (Fra) Groupama-FDJ 0:00:08
3 Emanuel Buchmann (Ger) Bora-Hansgrohe
4 Guillaume Martin (Fra) Cofidis
5 Nairo Quintana (Col) Team Arkea-Samsic 0:00:10
6 Miguel Angel Lopez (Col) Astana Pro Team
7 Daniel Martinez (Col) EF Pro Cycling
8 Mikel Landa Meana (Spa) Bahrain McLaren
9 Richie Porte (Aus) Trek-Segafredo
10 Egan Bernal (Col) Team Ineos