The event leader since Stage 3 had the luxury of starting 10th on the road with a cushion of almost 14 minutes over Pablo Quintanilla for the shortened, 167km special stage and the title never looked in doubt from there.
Brabec reached the Kilometre 69 waypoint second only to Cornejo, by just five seconds, and led Quintanilla by 18 seconds at Kilometre 119.
Kevin Benavides, meanwhile, had come to a halt just 19km into the special in what appeared to be a planned move to wait for Brabec, his team-mate, after the Argentine started the day almost four hours off the overall pace.
The Honda duo took the finish of the special together, with Brabec logging a stage time 53 seconds slower than Cornejo and 2:30s up on Quintanilla.
He is therefore the first American to win the Dakar and also breaks a streak of 18 consecutive victories for KTM.
“At the end, we put the pieces to the puzzle together,” said Brabec.
“It’s quite an accomplishment for America, for Honda, for the whole entire team. We couldn’t do it without every rider on the team, we couldn’t do it without the mechanics, and I’m excited.
“I was getting chills, like the last 30km. Just, the bike was working really good and I was really happy, really happy.
“To be here at the finish of the Dakar – my fifth Dakar, my second time finishing… I woke up this morning just happy to ride the last day and we’re here, we won.”
Quintanilla was fifth fastest on a day when he had to open the road again but wrapped up a career-best second position on his Rockstar Energy Husqvarna, making the Chilean a two-time Dakar podium finisher.Price dropped 3:24s relative to Cornejo to the first waypoint, putting the Red Bull KTM rider only 19th, before he rebounded to third for the day at 2:25s off the pace
The Australian ended the event 24:06s behind the winner but now has five overall podiums in six Dakar starts, including two victories, the exception being the 2017 edition when he broke his left leg.
Cornejo’s final day performance saw him take fourth position overall off another Dakar-winning factory KTM rider in Matthias Walkner, who gave up exactly six minutes through the stage and dropped to fifth in the general classification.
Luciano Benavides ended up one position behind his team-mate after Stage 12 having been fourth fastest on the day.
Rounding out the overall top 10 were Joan Barreda Bort (Monster Energy Honda) in seventh, from Franco Caimi (Monster Energy Yamaha), Skyler Howes (KLYMCIW Husqvarna), and Andrew Short (Rockstar Energy Husqvarna).
Australian Rodney Faggotter held on to 13th overall, 2:54:22s behind Brabec, on a Yamaha Motor Australia-backed entry.
Spaniard Jaume Betriu was the highest finishing rookie in 14th overall on his FN Speed Team KTM.
General classification: Bikes (Top 10)
|4||Jose Ignacio Cornejo Florimo||CHI||Honda||+0:31:43|
|7||Joan Barreda Bort||ESP||Honda||+0:50:57|