Sixteen-year-old wildcard Bencic, who is coached by Martina Hingis' mother, gave Watson a run for her money in the Californian desert and provided an idea of why she is one of the world's most promising youngsters.
Just 12 places separate the pair on the WTA rankings - Watson is at 134, Bencic at 146 - and it proved to be a tight match-up.
But in the end the British number three's gutsy performance - she saved four of eight break points - proved too much for the Swiss and victory was sealed in an hour and 38 minutes.
ATP Monte Carlo
Evans ends four-year wait to win on clay at Monte Carlo
A tough-looking tie with second seed Agnieszka Radwanska now awaits her.
Watson is the only Briton in the main women's draw in the Californian desert, having come through qualifying to secure her place.
Meanwhile, Peng Shaui of China sent 2009 champion Vera Zvonareva packing with a 4-6 6-0 7-5 win to set up a potentially exciting clash with Eugenie Bouchard in the next round.
Indian Wells results
First round
Casey Dellacqua (Australia) beat Christina Mchale (U.S.) 7-6(4) 6-4
Varvara Lepchenko (U.S.) beat Alison Van Uytvanck (Belgium) 6-2 6-2
Sharon Fichman (Canada) beat Shahar Peer (Israel) 4-6 6-3 6-4
Kurumi Nara (Japan) beat Allie Kiick (U.S.) 6-4 6-0
Yaroslava Shvedova (Kazakhstan) beat Chanelle Scheepers (South Africa) 4-6 6-4 6-3
Kristina Mladenovic (France) beat Zhang Shuai (China) 6-2 6-1
Madison Keys (U.S.) beat Tsvetana Pironkova (Bulgaria) 6-2 6-1
Heather Watson (Britain) beat Belinda Bencic (Switzerland) 7-5 6-4
Yanina Wickmayer (Belgium) beat Anna Karolina Schmiedlova (Slovakia) 3-6 6-2 6-4
Lauren Davis (U.S.) beat Chan Yung-Jan (Taiwan) 6-4 6-3
Bojana Jovanovski (Serbia) beat Alison Riske (U.S.) 3-6 6-3 6-3
Annika Beck (Germany) beat Stefanie Voegele (Switzerland) 6-2 2-6 7-5
Yvonne Meusburger (Austria) beat Iveta Melzer (Czech Republic) 6-4 6-2
Peng Shuai (China) beat Vera Zvonareva (Russia) 4-6 6-0 7-5
Silvia Soler Espinosa (Spain) beat Nadia Petrova (Russia) 1-1 (Petrova retired)
Shelby Rogers (U.S.) beat Petra Cetkovska (Czech Republic) 6-0 6-4
Tokyo 2020
Murray defends Olympic title in emotional win over Del Potro in 2016
ATP Monte Carlo
Medvedev withdraws from Monte Carlo after testing positive for Covid-19