Two-time Tour de France winner Pogacar chased in a pulsating late bid to reel in Schultz, and came within a whisper of winning at Sant Feliu de Guixols.
"I guess I messed that up, didn't I?" said Slovenian Pogacar, who came third in Saturday's Milan-San Remo, the year's first Monument race.
"But anyway it's nice to be here in the sunshine with a great peloton."
Israel Premier Tech rider Schultz was left shaking his head in disbelief after his audacious win.
"At 500m I looked around and decided to go and was surprised that a counter-attack wasn't coming," he said.
"I looked round with 100m to go and couldn't believe it, even at the finish line when I won."
On a slight upwards incline Pogacar crossed the line half a wheel behind but took six bonus seconds for second place.
The Slovenian also earned two seconds for an earlier sprint and was two seconds faster than the chasing peloton.
Targeting a Giro-Tour double in 2024, Pogacar began his build-up with an impulsive attempt to win the stage with scant regard to his overall chances, a tendency that makes him so popular with roadside fans.
There were four climbs on the 174km run that began and ended in the seaside resort in the Girona region and took 4hr 11min 38sec.
Resurgent Ineos Grenadier Egan Bernal won an intermediate sprint ahead of Pogacar along the way but was caught in a fall in the closing sprint.
The seven-day race concludes in Barcelona but is likely to be won in the mountain stages with the first gaps coming on Tuesday's stage two.
Tuesday's route will be much more mountainous and finishes at the Vallter ski resort after an 11km climb with an average gradient of almost 8 percent.
Wednesday's stage three has an 18km climb to the finish and stage six should decide the matter with a 6km climb to a mountain sanctuary at an average gradient of 7.2 percent.
