The pair, both born near Toronto and both of whom won the US Open as teenagers, battled for 2.5 hours on stadium court in an entertaining opening to the WTA and ATP combined tournament's main draw.
Andreescu, ranked 31st in the world, struck the ball with confidence and freedom as she dominated the first set, but Raducanu regrouped and fought back in the second.
The 2021 US Open winner went 5-3 up in the set after an epic game which secured with her seventh break point and went on to force a third set.
But Andreescu's power proved to be too much for the tiring Raducanu, who had shown promising signs of an upturn in form by reaching the last 16 at Indian Wells.
The Canadian has a tough test in the next round, where she will face seventh seed Maria Sakkari of Greece.
Italian Camila Giorgi needed three hours and 32 minutes to defeat Estonian Kaia Kanepi 7-6 (7/4), 6-7 (4/7), 7-6 (7/4), tying for the longest WTA main-draw match of the season.
Madison Brengle moved into the second round after Amanda Anisimova retired in the second set of their all-American encounter. Anisimova trailed 7-6 (7/5), 5-2 when she retired.
