Success is a wonderful thing, but too much success can be a curse of sorts.

When veteran musical artists who are defined by their hits go out on tour, they are often beholden to those signature songs.

Led Zeppelin lead singer Robert Plant famously once told the Los Angeles Times that his band’s iconic “Stairway to Heaven” makes him “break out in hives.”

But “the hits” are so often all fans want to hear. When artists play “the new stuff,” the old joke goes, that’s the time to go to the bathroom.

Bonnie Raitt has been very fortunate to have some success on the singles chart but not so much that her set list can’t wander into places unexpected. She played a sold-out show at the Blaisdell Concert Hall on Saturday night and part of the joy was the unpredictability.

Sure, most of Raitt’s hits made the cut, but her 1989 comeback single — the John Hiatt cover “Thing Called Love” — didn’t, and there were no calls for it from the audience. Raitt has built enough equity and trust with her fans that she can play what she wants and they will soak it up.

So when she opened her show with the first two tracks from her latest album, “Dig in Deep” — the blues-rock rave-up “Unintended Consequence of Love” and the INXS chart-topper “Need You Tonight” — the welcome was as warm as if she had started with her two biggest hits.

When she followed with a different Hiatt-penned song, “No Business,” the audience was game. Granted, “No Business” is off the top selling album of her career, 1991’s “Luck of the Draw,” but the point stands: The vast majority of Raitt’s 105-minute set was made up of songs the casual fan would not be familiar with, but Raitt’s hits do not own her — she owns her hits.

Two of her biggest are also from “Luck of the Draw,” and Raitt mixed it up a bit on both, rather than playing the album versions note-for-note.

Raitt kicked off a faster-paced “Something to Talk About” singing a cappella, and she took the reins off her vocals for the usually understated “I Can’t Make You Love Me.” Such departures are one of the things that make the live music experience so vital, and in that respect Raitt definitely delivers.

Though known more as an interpreter of songs than for vocal fireworks, Raitt showed on the oft-covered but never matched “I Can’t Make You Love Me” that she has the pipes to make a song soar.