Recent examples:
2014, A Raisin in the Sun (and Kenny Leon for directing it) over Twelfth Night and Glass Menagerie
2013, Kinky Boots not just for Best Musical but also Best Actor. Most people thought it would take Score and Choreography, but the other wins were more surprising.
2007, David Hyde Pierce (Curtains) over Raul Esparza (Company)
2005, Glengarry Glen Ross over Twelve Angry Men and Virginia Woolf for Best Revival
There have been a few years with surprising acting wins, often in the Featured categories if there's not a clear frontrunner, but I wouldn't call them "upsets." Examples such as Gabriel Ebert (Matilda), Ruthie Ann Miles (King & I) over all the Fun Home ladies, Levi Kreis (Million Dollar Quartet), Michelle Pawk (Hollywood Arms), Nikki M. James (Book of Mormon), Sara Ramirez (Spamalot), Paulo Szot (South Pacific), Denzel (Fences) over Alfred Molinda (Red), John Larroquette (H2$).
Waitress winning over Hamilton would have been the biggest upset in Broadway history, not unlike Crash over Brokeback Mountain at the Oscars. Mainly because Waitress probably wasn't even the #2 on most lists –– Shuffle Along was (and some people did think it would win Choreography and Costumes).