This year's Labor Day gas prices are the lowest since 2004, according to AAA. Even so, many of us will still be tempted to find ways to save even more. When you drive up to the pumps this holiday weekend, expect to see advertisements that promise discounts of 5 cents to 30 cents per gallon if you pay with a gas card offered by that gas station—places like Texaco or Chevron.

But don't kick yourself if you haven't signed up for one of their cards.

The reason? We took a look at these gas card deals from several big oil company brands and found that general purpose cash-back credit cards could deliver significantly better savings.

It may not be obvious that you can get more cash back from a bank rewards card than from a gas card. The reason for the confusion is that gas companies offer cash back in terms of cents-per-gallon while credit card companies offer cash back as a percentage of the amount you spend.

"Five cents a gallon looks good, but it's really tiny," says Patrick DeHaan, senior petroleum analyst for Gasbuddy.com, the leading smartphone app that helps consumers find the cheapest gas prices in their area.

Take Shell's "Drive for Five" gas card, for example. It pays 5 cents per gallon when you use it to buy Shell gasoline. Based on the recent $2.22 per gallon national average price for regular, a nickel back per gallon adds up to a discount of only 2.3 percent.

General Purpose Cash-Back Cards Pay More

A better alternative would be to get 5 percent cash-back savings on gas purchased using certain general purpose cash-back cards. Two good ones are the PenFed Platinum Cash Rewards Plus Visa and USAA Cashback Rewards Plus American Express.

The average U.S. household spent $190 per month on fuel for the year ending in June 2015, according to the latest data from the U.S. Bureau of Labor Statistics. Both of those cards would pay the average U.S. household an estimated $342 in cash back (after considering associated fees) over the first three years of use, according to our Credit Card Adviser Comparison Tool.

By contrast, the Shell gas card, we calculate, would return only $154 over the same three years, assuming the same fuel prices and monthly household gasoline expenditures for all cards.

There are gas cards that pay more—the ExxonMobile "Smart Card" program, for example, pays 6 cents per gallon, or an estimated $185 over three years. Still not as good as the PenFed and USAA cash-back credit cards.

Teaser rates set you up for another disappointment. Currently, the Chevron and Texaco gas cards pay 13 cents per gallon, but only for the 60-day introductory periodAfter that, the cash-back rate plummets to just 3 cents per gallon. Estimated three-year savings: $110.

The "Drive Savvy Rewards" associated with Phillips 66, Conoco, and others pay a 30 cent-per-gallon introductory rate. But again, that lasts only 60 days. Then, the cash-back rate drops to 10 cents per gallon for the next 30 days and then falls to 5 cents per gallon thereafter. Estimated three-year savings: $201.

How to Save the Most

Using a general-purpose cash-back card also gives you more freedom. You can earn cash back no matter what brand of gasoline you buy. With gas cards, however, your discounts are confined to only the card's single brand of fuel. 

Here's how to squeeze the most savings using a general-purpose cash-back credit card:

(Our comparison used the basic gas cards offered by four major oil companies, which can only be used at those brands' participating gas stations and have no annual fees. Our calculations assume that the balance is paid off in full each month to avoid high interest rates which can erode your cash-back savings. We did not consider other general purpose rewards credit cards also offered by oil companies which may have annual fees, carry the Visa or MasterCard logos, and can earn additional rewards points on purchases beyond participating gas stations.)