The top seed, who won the Cincinnati final a year ago over Jessica Pegula, increased her lead at the top of the WTA Tour match-win statistics as she secured her 49th of the season.
But the struggle was real for Sabalenka, who finished with two aces in the closing stages.
“I’m happy to get through this difficult match,” Sabalenka said. “I just hope tomorrow is a day off. I need time to recover from such a great battle.”
Raducanu put up a huge fight, matching Sabalenka throughout.
The British number one survived a 25-minute eighth game of the final set, which went to 13 deuces, with Raducanu saving four break points before finally holding for 4-all and eventually into a tiebreaker.
But Sabalenka squeezed out victory with a sixth ace for 5-4 in the breaker and delivered her seventh on second match point to bring the battle to a close after three hours and nine minutes.
“It was all about momentum,” Sabalenka said. “I took some risks at the end, went for crazy shots, went to the net.
“A risky game from me helped to put a lot of pressure on her,” she said of an opponent whom she hugged warmly at the net.
Sabalenka is bidding for her 10th trophy at the 1000 level and second this season after winning at Madrid.
In other third-round results at the last major tuneup prior to the US Open, Ekaterina Alexandrova defeated Australian Maya Joint 6-4, 6-3.
Sorana Cirstea defeated Yuan Yue of China 6-7 (2/7), 6-4, 6-4 and will next play third seed Iga Swiatek, who got a walkover into the round of 16.
Spain’s Jessica Bouzas Maneiro, a quarter-finalist this month in Montreal, made further hard court progress with a 6-4, 6-1 thrashing of American wild card Taylor Townsend.
Her next opponent will be Sabalenka on Wednesday.
In the men’s draw, seventh seed Holger Rune, a semi-finalist here a year ago, ended the hopes of Alex Michelsen with a 7-6 (7/4), 6-3 victory.
Felix Auger-Aliassime got a win for Canada, advancing 7-6 (7/4), 4-2 when French opponent Arthur Rinderknech retired with apparent heat illness after two gruelling hours on court.
American Frances Tiafoe advanced past Ugo Humbert of France 6-4, 6-4 in 82 minutes. (AFP)