The Italian has now won 26 consecutive sets in Masters 1,000 tournaments, surpassing Novak Djokovic, who previously held the record with 24. Janik broke Novak's record by winning the opening set, and equaled it in the previous round.
Siner broke his opponent twice in the first set, while in the second set he made the difference in the fifth game, when the world number two used the fourth break point.
The 2024 champion will play in the round of 16 against home player Alex Mikkelsen, who eliminated Alexander Tabil 2:1.
"I'm very happy," Siner said after the victory, adding:
"This sport is unpredictable, so we're trying to stay as focused as possible and we'll see what the next round brings."