The so-called translunar ignition came on Thursday night, 25 hours after liftoff, putting the three Americans and a Canadian on course for a lunar fly-around early next week.
Their Orion capsule bolted out of Earth orbit right on cue and chased after the moon nearly 400,000km away.
It was the first such engine firing for a space crew since Apollo 17 set out on that era's final moonshot on December 7, 1972. NASA said preliminary reports indicate it went well.
"Humanity has once again shown what we are capable of, and it's your hopes for the future that carry us now on this journey around the moon," said Canadian astronaut Jeremy Hansen.
He said they were glued to the windows to take in the view, calling it "phenomenal".
NASA had the Artemis II crew stick close to home for a day to test their capsule's life-support systems before clearing them for lunar departure.
Now committed to the moon, the Artemis II test flight is the opening act for NASA's grand plans for a moon base and sustained lunar living.
Commander Reid Wiseman, pilot Victor Glover, Christina Koch and Hansen will dash past the moon then hang a U-turn and zip straight home without stopping on land.
In the process, they will become the farthest humans have ever travelled from Earth, breaking the Apollo 13 distance record set in 1970. They also may become the fastest during their re-entry at flight's end on April 10.
Mission Control gave the final go-ahead minutes before the critical engine firing, telling the astronauts that they were embarking on "humanity's lunar homecoming arc" to bring them back home.
The engine accelerated them to 38,000km/h to shove them out of Earth orbit.
The next major milestone will be Monday's lunar flyby.
Orion will zoom 6400km beyond the moon before turning back, providing unprecedented and illuminated views of the lunar far side, at least for human eyes. The cosmos will even treat the Artemis II astronauts to a total solar eclipse as the moon temporarily blocks the sun from their perspective.
While awaiting their orbital departure earlier on Thursday, the astronauts savoured the views of Earth from tens of thousands of kilometres high. Koch told Mission Control they could make out the entire coastlines of continents and even the South Pole, her old stomping ground.
NASA is counting on the test flight to kickstart the entire Artemis program and lead to a moon landing by two astronauts in 2028. Orion's toilet may need some design tweaks before that happens.
The lunar loo malfunctioned as soon as the Artemis crew reached orbit on Wednesday evening. Mission Control guided astronaut Koch through some plumbing tricks and she finally got it going, but not before having to resort to using contingency urine storage bags.
Controllers also managed to bump up the cabin temperature. It was so cold earlier in the flight that the astronauts had to dig into their suitcases for long-sleeved clothes.
