A powerful bunch was still together as the 181-kilometre fourth stage slogged up Jebel Jais, the highest point in the Emirates.
Even though the gradient steepened to 7 per cent in the last 200 metres, the Slovenian, led out by two of his UAE team-mates, charged away.
Briton Adam Yates of Ineos and Russian Aleksandr Vlasov of Bora gave chase in a frantic uphill sprint, but could not close the gap. The trio finished three seconds ahead of the next group of the shattered bunch.
Pogacar, the defending UAE champion, took the overall lead from Swiss rider Stefan Bissegger who was dropped earlier on the climb.
Pogacar, a double Tour de France winner, leads Filippo Ganna of Ineos by two seconds.
The Italian time-trial specialist managed to stay with the leaders on the climb and surged to the line in a desperate attempt to close the gap Pogacar had created.
Vlasov is 13 seconds off the lead in third with Yates another two seconds back.
Thursday's fifth stage will cover 182 kilometres from Ras al Khaimah Corniche to Al Marjan Island and is likely to end in a sprint.
The race ends Saturday with another stage that finishes with a potentially decisive climb.
