A new headline-grabbing report reveals the amazing power of two crucial “fat swaps” to protect guys against fatal prostate cancer. We think this way of eating could slash breast cancer risk, too.

Just make two changes:

1. Choose vegetable-based fats such as extra virgin olive and canola oil, nuts and seeds, avocado over animal fats.

2. Replace some of the carbs on your plate with vegetable fats, too.

That’s right. This new report, which is impressive because it followed nearly 5,000 guys with prostate cancer for more than eight years, found that men who cut their daily carbs from sweets and starches like bread, pasta and crackers by just 10 percent and replaced those calories with healthy vegetable-based fats slashed their risk for lethal prostate cancer by 29 percent. They also lowered their overall risk for fatal health problems 26 percent.

Guys who went for veggie fats instead of fatty meats, butter, ice cream, cheese or processed foods got a big bonus.

Those who ate the most vegetable fat daily had a 55 percent lower risk for aggressive prostate cancer than those who ate the least. But those who ate the most animal fats and trans fats had a 35 percent higher risk for aggressive cancers than those who ate the least.

That’s big news for the 2.5 million men living with a diagnosis of prostate cancer, and the one in six who will receive a diagnosis during their lifetime.

We suspect that the same good-eating plan can help women battle breast cancer, too, because research has consistently shown that the same healthy steps protect against both of these hormone-driven cancers.

Putting fewer refined carbs into your digestive system means lower blood sugar and lower levels of insulin, a hormone that at high levels can spur the growth of cancer cells.

Refined carbs, trans fats and saturated fats also increase levels of body-wide inflammation, which can increase your risk for cancer and spur cancer on.

In contrast, veggie fats cool inflammation and deliver a big dose of disease-fighting nutrients.

Now, all fats are high in calories. That’s why swapping is so important; keep calories steady while you amp up the good stuff.

Great ways to swap in vegetable-based fats at mealtime:

Breakfast: Go nuts first thing in the morning. Instead of two pieces of toast, top one piece of whole-grain toast with nut butter. Instead of low-fiber cereal, switch to plain, nonfat yogurt with chopped walnuts, ground flax or chia seeds and sweeten it with berries, peaches or melon chunks.

Lunch: Upgrade your sandwich. Instead of cheese, tuck avocado slices into your sandwich. Opt for peanut butter or almond butter instead of lunchmeat. Use one piece of bread instead of two, and spend the saved calories on an extra tablespoon of peanut butter or extra avocado.

Dinner: Skip a starch. Replace a starch (such as white potato, white rice or pasta or bread) with sliced avocado (spritzed with lemon juice) or with a small green salad. Top it off with a drizzle of olive oil and a sprinkle of walnuts, ground flax or chia seeds. Bread chicken or fish with toasted, finely chopped nuts (or with cornmeal mixed with ground flaxseed) instead of flour. Then bake.

Mehmet Oz, M.D. is host of “The Dr. Oz Show,” and Mike Roizen, M.D. is Chief Wellness Officer and Chair of Wellness Institute at Cleveland Clinic.