There are two ways to win big at Chariot race:
1. Play it more often. Let's say that on a random draw you win 60% of the time. I can still win the chariot race if we both draw deck and I win the split 6-4. Each turn you will expect to gain 2.4 VP (4 * .6) while I will expect to gain the same (6 * .4) if we both draw our decks. But suppose our decks are assymetric - you have provinces and banks while I do not. If you play one fewer Chariot a turn, I can slowly build up a lead. This is actually surprisingly simple to execute for good returns. If I can build a faster/better engine through draw luck (e.g. a 3/4 Iw/Steward/Smithy/Village and you get a 5/2), card choice (e.g. Xroads/Ghall/Wshop/Ratcatcher vs Xroads/Rabble), or execution (Chouse/Cellar/Shuffle control) then I can treat the Chariot races as non-terminal mini-monuments - they give me cash and VP, just not all the time. Remember in a 20 card deck, having an extra 4 Ports compared to 2 Silvers is not going to give you that many more win chances - you will only draw them on 1/6 Chariot plays and they will win on only some subset of those, far better to play another Chariot race. Also, building an engine with lots of Craces means that you can let the game drag, eventually you will overtake your opponent on VP if they cannot end the game.
2. Control the top deck. Obviously there are strong cards for hammering the other guy's top deck: Spy, Pool, Oracle, and Sea Hag all do quite well here in the early game things like Rabble and Fteller also work decently (particularly if you trashed your coppers).
You can also easily get a lot of mileage out of top decking cards: Count, Mandarin, Scavenger, and Courtyard all can let you drop your highest value card on deck for a much higher odds of winning.
Less powerfully, but far more common, are reordering and informational cards like: Apothecary, Cartographer, Wwell, Navigator, Wmnstrl, Mystic, Scout, etc. these at minimum let you decide to play your Crace now or at some point later in your deck when you are more likely to hold a higher than average card on top deck, with discarding this lets you more quickly sort through the deck, and reordering, of course, lets you search a drastically larger space for your high point cards (which is why Apothecary/Crace is good - you can top deck a big green and forget about it).
Another common shot are top deck gainers, some are low quality, like B-crat or Armory, that stop being useful once you both have a good block of cards at better than $3, but others are insanely powerful: Blocked tournament? Gain a Duchy, Crace with a known $5 and discard that pesky green. Wt, again, combos with everything - Forge a province, top deck it, and then Crace. Graverobber - ehh maybe, particularly if you are pulling Duchies out. Taxman? Well you miss out on your Gold/Silver/Plat initially ... but this is insanely good with a Crace once your can draw deck, it is totally worth it to Plat -> Plat to Crace when you are deck drawing, likewise Bag of Gold can make you race with $6.
Which of course gets to our final, and arguably most common setup - draw your deck & discard something big so it is your only card in the draw deck. Say I have a bog standard Smithy/Village/Wshop/Cellar setup. Okay, I buy a Province (no +buy so this is not too hot against BM/Smithy). Next turn, I Wshop a Crace then use Cellars when it is the only card in the discard/draw deck to discard the province and draw the Crace (I may have to discard the Prov 2x). Now I have an all but unbeatable Crace target ... and I can hit for an additional Crace go every turn as long as I can maintain the draw. The setups here are legion - Htraders, Hamlet, Oasis, Stables, Plaza, Library, Adventurer, Schamber, Vault, Whouse, Golem, Farmv, Yw, Hparty, Embassy, Inn, Dungeon, Artificer, Forum, and likely a few more I missed, but most anything that has high odds of allowing your to leave a big value card as the only thing in the discard can work well (e.g. Hparty that leaves a bunch of Hparties in the discard, Adventurer that leaves nothing but provinces, or Golem that leaves some Golds). Setting this up takes a bit, but from then on out you can pretty much engineer whatever high card(s) you want to be in the discard and then just slam Craces until they pile out or you run out of draw potential. Yeah they are less than half as efficient as Monuments, but they are vastly better on low +action boards.
Is Crace actually overpowered? No. Unlike with Monument it takes a lot of Craces to generate Province level points and Crace is abysmal buying power in the early game, but it has the virtue of letting you build to unlimited VP potential - often your only shot at winning if the other guy grabs too much green too quickly on a lot of boards. Shoehorning in very strong Crace setups mid-late game is quite doable on a lot of boards. I have not played enough to know, but I strongly suspect that Crace should generally be played by first building a really strong engine, then being able to play many Craces, and then trying to increase your Crace odds (obviously some cards will let you do multiples of these like Apothecary). Just increasing the value density of your deck seems weak and going for a cute combo (like Courtyard) seems insufficient on its own. Crace's single biggest asset is that you can play buckets of them as long as you have the draw - so get the draw first.