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.

Raitt played half of the dozen tracks from “Dig in Deep,” but she also took her audience back to her early days with several selections from her ‘70s catalog, going as far back as her eponymous debut album, plucking “Women Be Wise” from that one, and getting a nice assist from the horn section of opening act the California Honeydrops, whom she lavished praise on.

That generosity was a staple of the evening. Raitt ceded the spotlight to her crack backing band often, even going so far as to let keyboard player Mike Finnigan take the lead on a cover of B.B. King’s “Don’t Answer the Door.” Finnigan was a revelation, providing stunning blues vocals. Raitt’s fans seemed genuinely pleased to see a member of her backing band — each of whom has played with her for more than 20 years — take a turn in the spotlight.

Raitt and her band have built up chemistry over the years, and that they enjoy playing together comes across live, whether it’s her going face-to-face with guitarist George Marinelli or chatting with bassist James Hutchinson about how long he’s lived on Maui (Her: “Has it been 7 years now?” Him: “15.”) Drummer Ricky Fataar rounds out her marvelous backing quartet.

Raitt also shared plenty of banter with the audience, mostly about how much she loves Hawaii — the fragrance of her lei, early-morning swims, the relaxed attitude — but also backstory about some of her songs and joking that she was heading Down Under to play “Need You Tonight” for Australians — maybe only AC/DC can match INXS among that country’s greatest bands. “I can handle it,” she said of the song she’d been wanting to record since it came out in 1987.

That self-assuredness is no surprise. After four decades in the spotlight and acclaim as the world’s greatest slide guitarist from no less an authority than the legendary B.B. King, Raitt strides the stage with confidence. She knows she has the chops and focuses on the music. Where other performers might change outfits every other song, Raitt changes … guitars, constantly switching instruments to get the right sound for each number.

Her one nod to appearance was joking that she had to put on lipstick for her closer, “Your Sweet and Shiny Eyes,” after giving the audience permission to take pictures and shoot video, which brought out dozens of cameras for that track from 1975’s “Home Plate” album as well as her band’s bows.

Raitt also brought the California Honeydrops back out for some love from the audience. The Oakland quintet were quite a find, with a 45-minute set that won over the audience quickly.

The Honeydrops deliver a genre-crunching brand of jazz-rock, led by Lech Wierzynski’s soulful vocals. Wierzynski (who also played trumpet and guitar) and Johnny Bones on tenor saxophone get most of the attention and most of the solos, but keyboardist Lorenzo Loera, drummer Ben Malament and bassist Beau Bradbury are also key to their tight sound.

One highlight was Wierzynski’s story about the band’s beginnings nearly 10 years ago, busking in Bay Area subway stations. Malament and his drum kit were turned away at the entrance, leaving him to come back the next day with a washboard, which he produced again Saturday night for the bawdy (in a WWII-era way) “Do It Like That.” The whole lot of them are charmers, almost too big to be opening for anyone much longer. They might have made enough fans Saturday to come back through the islands on their own before long.

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