After three sets and almost three hours of play, Tiafoe won 7:6 (4), 4:6, 7:6 (11).
In the first tie-break, the American used the fourth set point and went up 7:4 to 1:0.
Menšík fought back in the second set, and the decisive break came in the ninth game, when Cech converted his fourth break point. This was also the only break of the entire match.
The servers dominated the deciding set, and in the dramatic tie-break, Jakub missed two match points, while Tiafo used his seventh.
Frances will play in the round of 16 against Frenchman Terence Atman, who surprised seventh seed Felix Auger-Aliassime with a 2:1 (6:3, 1:6, 6:3).
Aleksandar Zverev defeated Marin Čilić for the eighth time in a row – it was 2:1 for the German – 6:2, 5:7, 6:4 after just over two and a half hours of tennis.
Zverev will play against world number 111 Quentin Alis in the quarterfinals.
Round of 16 pairs:
Sebastian Korda – Martin Landaluse
Jiri Lehecka – Taylor Fritz
Tomas Martin Ečeveri – Tomi Pol
Valentán Vachero – Artur Fis
Igo Amber – Francisco Serundolo
Quentin Alis – Aleksandar Zverev
Terens Atman – Franses Tijafo
Janik Siner – Aleks Mikelsen
