Rune struck a crosscourt backhand netcord winner to hold serve and take the set.
Serving down 2-3, the 21 year old Rune held multiple game points before he committed several errors including striking a backhand volley long and hitting a down the line forehand long.
The 22 year old Stricker broke serve to lead 4-2 before holding serve to lead 5-2.
Rune then struck several backhand winners and aces to win the next three games in a row to level set at five games all.
Stricker held serve to lead 6-5 before Rune struck an ace down the tee on game point to hold serve and enter the tiebreaker.
Stricker hit a down the line forehand winner to lead 1-0 before netting two crosscourt passing shots on the following two points to trail 1-2.
Rune struck a crosscourt backhand passing shot winner to lead 3-1.
Then after Rune had earlier given several high fist pumps up in the air, it was time for his mother Aneke Rune to also give a high fist pump in the air from the stands.
Rune struck an open stance crosscourt forehand passing shot winner while on the run to lead 5-1.
Stricker hit an inside out down the line swing forehand volley long to end the match after one hour and twenty-six minutes of play.
In Friday's quarterfinals not before 9:00am PST USA, the 14th ranked Rune faces the 54th ranked David Goffin of Belgium.