Do tomato-based sauces change/enhance flavour when left in the fridge?

Most sauces, tomato based or not, will improve in flavour after being left overnight. This is also true of stews and casseroles. The received wisdom is that it gives the flavours a chance to 'marry' and blend, though I'm not sure of the science behind it.

Cells are complex. Each one is a unit which needs to keep itself alive and achieve homeostasis with its environment (big picture: tomato vs. world, small picture: tomato vs. other cells). To this end they need an assortment of proteins and other compounds.

Some nutrients are in a plant due to the nature of the the organ the tissue it is a part of: the tubers contain cells with organelles which contain carbohydrates due to their function as an energy store, while fruiting bodies often contain chemicals (and the enzymes which form the metabolic pathway to create them) which act on the behavior of the animals eating them. A good example would be the tobacco plant and nicotine, which is a pesticide; more mundane examples are herbs.

When you cut the fruiting body of a plant you lyse some of the cells where you have cut. Pureeing the fruiting body lyses many more, and the vacuoles in the cell which store digestive enzymes (for breaking down unneeded cellular structures - tomatoes aren't carnivorous) occasionally break and begin acting upon whatever is around them. This is why cut apples brown and why cut fruit and prepared herbs lose their flavor.

But why does it taste better? The most likely explanation is that this allows the digestive enzymes to break down the contents of the sauce, some of which are indigestible. This makes the sauce more nutritious and easier to digest and your tongue notices.

For reference see this patent which mentions the use of pectinase to prepare a tomato sauce. Pectin binds cells together and is an indigestible fiber. The process would convert some of the pectin in the prepared tomatoes into digestible carbohydrates.

It is a well known phenomenon. Many sauces, stews, casseroles, etc. improve as flavours develop over time due to chemistry. Breads also can improve if left to proof slowly before baking.

I do most of the cooking in our house, and I'd have to say it's true. When I'm making a jumbalaya, spaghetti sauce or goulash, all of which have tomato-based sauce, my wife always comments that leftovers the next day taste better than the night I made it. The same for my pulled pork, where I use a tomato and BBQ based sauce. I can't notice the difference myself, chiefly because I eat like a pig, but I trust my wife's judgement.

I'm not sure of the mechanism involved, whether it's some kind of "marrying" or settling process one of the other contributors posited, or whether it's simple placebo or expectation... but it works.

It's not just about tomatoes. This is a well-known phenomenon.

I used to be a professional chef, and the recipes for the soups in one particular restaurant I worked in called for resting overnight.

One night, a particular soup ran out. A server took an order for it anyway even though he had been told it was 86'd (gone), because he knew there had been a pot of it cooking in the prep kitchen just before opening time.

Imagine the drama when he was told that he'd have to go tell his diner "Sorry" because the soup wouldn't be done till tomorrow.