Rafael Nadal celebrates
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Daniel, ranked 121 in the world, looked unfazed on Arthur Ashe as he took the opening set against the top seed, and he could have gone further ahead having broken Nadal early in the second.
However, the Spaniard responded with two breaks of his own en route to taking it 6-3, and he wrapped up the third in just 33 minutes to edge towards victory.
The two-time champion capitalised on Daniel's fatigue to wrap up the win in the fourth set. Nadal goes on to face Leonardo Mayer in the third round after the Argentine beat Yuichi Sugita in four sets.
Daniel had never gone beyond the second round at a Grand Slam, but he hit 11 winners on his way to taking the first set in hugely impressive fashion.
The 24-year-old went on to break Nadal once again in the second set, but the 31-year-old responded in champion style to win five of the next six games.
Nadal turned the screw and broke Daniel twice on his way to clinching a speedy third set, and it was a double fault from the latter which allowed the Spaniard to break again in the fourth.
As Daniel started to tire, Nadal took full advantage, breaking his opponent once more before sealing the victory at 12.29am local time.
Eliteserien, Round 6
Eliteserien, Norwegian Commentary