Roglic lost out to Evenepoel at the Tour of Spain last season and the pair are using this race as a warm-up for their big showdown at the Giro d'Italia.
One of Evenepoel's main strengths is acceleration sustained over a long stretch that few in cycling can live with, but on Friday, Roglic won with his own trademark, a short, late acceleration near the finish line.
With sections of this slope at 15 per cent, when the veteran Slovenian went for the line the young Belgian was unable to follow and lost six seconds plus the four seconds in bonuses and trails by ten seconds overall.
Evenepoel had tried several times on the 8km climb to gently pull away, but Roglic always responded and bided his time.
"I really had to hold on at times," he said. "So I'm totally happy with that win."
The UAE Emirates pair Joao Almeida and Marc Soler were 12 and 25 seconds adrift. Had their team leader Adam Yates not fallen on the first day one of that team could have been leading.
There are two stages remaining, with Saturday's run largely flat meaning the race will go down to the final stage in downtown Barcelona.
The packed crowds that usually show up will be able to see the pair slug it out on the repeated climbs of the Montjuic mountain in the Catalan capital.
