It touched down at 7.56 am (AEST) to loud cheers in mission control.
This is the most sophisticated rover the agency has ever sent to the Red Planet.
It will gather data and look for signs of ancient life in a crater that once contained a lake about 3.9 billion years ago.
The landing of the six-wheeled vehicle marks the third visit to Mars in just over a week.
Two spacecraft from the United Arab Emirates and China swung into orbit around the planet on successive days last week.
All three missions lifted off in July to take advantage of the close alignment of Earth and Mars, travelling some 300 million miles (more than 482 million kilometres) in nearly seven months.
Perseverance, the biggest, most advanced rover ever sent by NASA, stood to become the ninth spacecraft to successfully land on Mars, every one of them from the US, beginning in the 1970s.
The car-size, plutonium-powered rover was aiming for NASA’s smallest and trickiest target yet: a five-by-four-mile strip on an ancient river delta full of pits, cliffs and fields of rock.
Scientists believe that if life ever flourished on Mars, it would have happened three billion to four billion years ago, when water still flowed on the planet.
Percy, as it is nicknamed, was designed to drill down with its seven-foot (two-meter) arm and collect rock samples that might hold signs of bygone microscopic life.
The plan called for three to four dozen chalk-size samples to be sealed in tubes and set aside on Mars to be retrieved by a fetch rover and brought homeward by another rocket ship, with the goal of getting them back to Earth as early as 2031.
Scientists hope to answer one of the central questions of theology, philosophy and space exploration.
“Are we alone in this sort of vast cosmic desert, just flying through space, or is life much more common? Does it just emerge whenever and wherever the conditions are ripe?” said deputy project scientist Ken Williford.
“Big, basic questions, and we don’t know the answers yet. So we’re really on the verge of being able to potentially answer these enormous questions.”
China’s spacecraft includes a smaller rover that also will be seeking evidence of life — if it makes it safely down from orbit in May or June.
Perseverance’s descent has been described by NASA as “seven minutes of terror,” in which flight controllers can only watch helplessly.
The pre-programmed spacecraft was designed to hit the thin Martian atmosphere at 19,500 km/h, then use a parachute to slow it down and a rocket-steered platform known as a sky crane to lower the rover the rest of the way to the surface.
Mars has proved a treacherous place: In the span of less than three months in 1999, a US spacecraft was destroyed upon entering orbit because engineers had mixed up metric and English units, and an American lander crashed on Mars after its engines cut out prematurely.
NASA is teaming up with the European Space Agency to bring the rocks home.
Perseverance’s mission alone costs nearly US$3 billion ($3.86 billion).
The only way to confirm — or rule out — signs of past life is to analyse the samples in the world’s best labs. Instruments small enough to be sent to Mars wouldn’t have the necessary precision.
“The Mars sample return project is probably the most challenging thing we’ve ever attempted within NASA,” said planetary science director Lori Glaze, “and we don’t do any of these things alone.”