Nadal, playing his first match since losing to Roger Federer in the Wimbledon semi-finals, fell behind 5-2 in the tiebreak before roaring back to prevail in his first career meeting with world number 53 Evans.
Frenchman Benoit lost his temper in the third game of the second set when top seed Tsitsipas halted the match to attend to a broken shoe lace.
Roger Federer returned from a month-long layoff with a 6-4, 6-4 second round victory over Roberto Bautista Agut on Tuesday at the Western and Southern Open in Cincinnati.
A summary of sports events and persons who made news on Monday
Roger Federer glided to victory on another hot, steamy day at the US Open, the envy of a clutch of men's players made to work overtime on Tuesday at the season's final Grand Slam.
Former world number one Garbine Muguruza was beaten 7-5, 6-4 by Aryna Sabalenka in the China Open second round on Tuesday while an ailing Jelena Ostapenko lost 6-0, 6-0 to Wang Qiang.
Photos from matches played Day 7 of the Australian Open at Melbourne Park on Sunday
Cilic's booming serve lacked its usual accuracy and Germany's Kohlschreiber was able to control long rallies, pushing the towering Croatian around the court with pinpoint groundstrokes en route to a quick victory.
IMAGES from Day 8 of the US Open on Monday
IMAGES from the matches played during the Wimbledon Championships at the All England Lawn Tennis and Croquet Club, at Wimbledon in London on Thursday
The ATP issued the latest men's tennis rankings on Monday and the top 10 list remains unchanged with Serbian tennis ace Novak Djokovic still leading the rankings.
Images from matches played on Day 5 at the Australian Open in Melbourne Park on Friday
Fourth seed Angelique Kerber's bid for consecutive Grand Slam titles ended when 29th seed Dominika Cibulkova defeated the German 3-6, 6-3, 6-3 in the US Open third round on Saturday.
Summary of sports events and persons who made news on Tuesday
Images from Wednesday's matches at Roland Garros