Leaving the mats in and closing the windows may lead to the fumes getting everywhere (worse than before perhaps) in the car.
Take the mats out. What I propose will make a MESS, so be prepared.
I'm going to go through the various things you may have at home:
The problem with using baking soda is that the baking soda is an ionic compound and doesn't dissociate and thus doesn't react to the gasoline (gas is a mixture of various hydrocarbons, which are NOT ionic--remember: like dissolves like). You need something that will bind to the gas, react with it, and thus either change it to something that isn't noticeable or something that is much easier to get out.
You could try 70% alcohol. However, as it has SOME but NOT MUCH miscibility with gasoline, it probably won't work well. It can additionally discolor the mat or otherwise have undesired effects with it. Alcohol can and does work for some organic compounds, however.
Acetone should work quite well; it is commonly thought of as a "universal" solvent, especially with organic compounds. USE GLOVES!! I cannot stress this enough, as it can easily carry crap through your skin and into your blood stream if you are not careful. (There are worse compounds that will do this, but they are not commonly found in the household.) Acetone can and will attack plastics, so if your mats are plastic then acetone is probably NOT what you want; test on an inconspicuous place. This has a rather high probability of not working because of this problem. [See ** and ***]
You could try dish soap. Dish soap is specifically engineered to handle greasy stuff, which you could easily call gasoline greasy. It can take a fair bit, and will need a lot of water to wash it out thoroughly depending on how the mat is made, but shouldn't really affect the color of the mat (unless the mat is not color safe, which the exposure to gas should show you
).
You could try something like SimpleGreen, or some other degreaser used in the garage and car industries.
I would try SimpleGreen, followed by a bit of dish soap to ensure I got as much as possible out. If the gas stained the mat, you may try something like alcohol to get it out. Then, I would take a box of baking soda and generously sprinkle it on the mats. Take a scrub brush and brush the baking soda into the mat; repeat it until the mat appears almost white. Yeah, it's probably overkill, but you want that smell gone entirely. Give it a few days in an open area (or in the sun, if good weather is expected) to dispel any fumes that may make it out of the mat. Thoroughly wash the baking soda out, allow it to dry, and replace it in the car. If I'm feeling adventurous, I might try acetone BUT that has a rather high possibility of failure (see above).
** For giggles, you can place some acetone in a container (preferably glass, but something you don't really care about), and place a styrofoam cup in the acetone. The acetone will dissolve the styrofoam and make a mess, but you will see the cup slowly get smaller and smaller as it is eaten and dissolved from the bottom upward. A sciency trick for the kids.
*** I had a laser level at one time, until the cat knocked the acetone can over and spilled acetone on it. The cat was trying to jump to the top of the cabinets and missed, sliding downward to the counter top and knocking over the acetone I was working with. The laser level nearly instantaneously fused into a chunk of melted plastic, rendering the laser inoperable. I couldn't really get mad at the cat as she was a rescue that someone had thrown out after declawing her. I didn't see what she was trying to do until too late, or I would have tried to stop her. She was trying to jump from the washing machine behind me to the top of the cabinets mounted on the wall in front of me. She was a good cat.