At the 10.6 km mark the Frenchman had opened a lead of 16.3 seconds over Germany's Arnd Peiffer and by the time he arrived at the fourth shoot he had almost two minutes to spare.
Martin Fourcade - Pyeongchang
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Despite having skied and shot superbly until that point, Fourcade missed his last two shots, incurring two minutes in penalties and giving himself a mountain to climb to put himself back in contention for the gold.
Boe went out ninth of the 86 starters and an early miss left him with pertly of work to do, but his powerful skiing allowed him to win back the time lost due to his errant shooting and he could even afford another late miss without ruining his chances.
With the temperature dropping steadily through the evening, the Norwegian had to endure a long wait at the finish line as his rivals fell away one by one.
Sweden's Sebastian Samuelsson, who won a silver medal in Monday's pursuit, put in another strong performance and was in with a shout for bronze, but he was edged out of the medals when Fak put in a powerful spurt after the final shoot.
Both Fak and Landertinger shot clean on the night but Boe's superior skiing took him clear. For a while gold looked within his grasp but he could not quite maintain the pace but still finished strongly for his first Olympic medal.