Derek Carr's Wife -- Cops to the Rescue ... In Gas Tank Debacle

Derek Carr didn't run out of gas Sunday during his huge win over the Broncos -- his wife, not so much.

While the Oakland Raiders QB was leading his team to victory in Denver, Heather Carr (who's pregnant) was driving home with their kid and dog in the car ... when they ran out of gas on a freeway off-ramp.

The Dublin PD tells TMZ Sports ... an officer in the area noticed Carr's car on the side of the road and stopped to check out the situation -- and ultimately got her enough gas to get her to a gas station.

We're told the officer tracked down a gas can and had it filled -- then brought it back to Heather ... and by the way, the officer had no idea the woman was the wife of an NFL quarterback.

"In this day and age, we do a lot more than catch the bad guy," a spokesperson for the PD tells us.