The Court Two clash had barely begun when showers stopped play and both players swapped early breaks having returned after a delay of a little more than an hour before Siegemund took full control by moving through the gears.
The 37-year-old edged in front when Sierra produced a double fault and then unleashed some huge serves to hold for a 5-3 lead in the next game, wrapping up the set with another break in the ninth game.
Sierra, bidding to become the first lucky loser to make the quarter-finals of a Grand Slam, found herself in big trouble at 0-3 down in the second set following another rain delay and she buried her face in her towel during a break.
Siegemund was in no mood to show mercy to the world number 101, however, as she pushed on and closed out the victory on her third matchpoint to book a last eight meeting with either top seed Aryna Sabalenka or Belgium's Elise Mertens.