The Belarusian seized on four of six break-point opportunities to win 6-4 6-1, following up her victory over the same opponent at the same stage of the US Open in September.
In New York, Mertens surprisingly won only one game as Azarenka produced a performance that overwhelmed the 24-year-old, and although this clash was a more close-fought affair in the first set, eventually it became a rout.
Azarenka said afterwards: "I feel she adjusted her game a bit from New York, so it took me a bit of time to adapt to that."
She added: "Today I didn't expect the same result, but I did feel like I was really in control after I adjusted my game – I felt I made it very difficult for her to earn points."
Former world No.1 Azarenka finished runner-up to Naomi Osaka at the US Open but took the title at the Western and Southern Open event, also held at Flushing Meadows in the run-up to the grand slam tournament.
The WTA season only resumed in August, having been halted in March amid the COVID-19 pandemic.
Greek player Maria Sakkari, who took a set off Serena Williams at the US Open, scored an impressive 3-6 6-3 6-1 victory over Tunisian Ons Jabeur and will face Azarenka next.
American Jennifer Brady, another who made her mark in New York by reaching a maiden grand slam semi-final, dug deep to see off impressive Russian qualifier Veronika Kudermetova in three sets.
Kudermetova, who beat second seed Karolina Pliskova in the second round this week, could not build on a strong start to the quarter-final tussle as she exited 6-7 (5-7) 6-3 6-1.
Brady will face Aryna Sabalenka in Saturday's last-four matches after she defeated Sara Sorribes Tormo 6-0 4-6 6-0.