Live: Matchbox Twenty with Alanis Morissette and Mute Math

It’s good to be Matchbox Twenty. The band feted this fact with a triumphant two-hour set Sunday night at the Staples Center. Supporting its 2007 greatest hits album, “Exile on Mainstream,” with the band’s first national tour in more than four years, the quintet tapped unlikely but compelling openers Alanis Morissette and up-and-coming alt rock group Mute Math for an eclectic, heartfelt show.

After more than 10 years together and 28 million albums sold worldwide, Matchbox Twenty approached its latest release as its swan song but instead discovered a new sense of unity in the studio. Rather than simply serving as a vehicle for material by frontman Rob Thomas, whose 2005 solo album ” . . . Something to Be” also achieved multi-platinum success, the band collaborated fully for the first time on six new songs. This newfound solidarity came through during the band’s tight, congenial performance.

Promising an adoring audience the chance to forget the world’s horrific happenings, Thomas drew fans into the bubble of the band’s likable, if at times overly safe, reality. Other than the new single “How Far We’ve Come,” a spry pop-rock anthem about the end of the world, the band stuck close to the personal all night. Thomas emoted his way through new songs, including hooky, piano-laced “If I Fall,” and humorous ode to married life “I’ll Believe You When,” as well as abundant hits, such as moody ballad “Back 2 Good” and acoustic guitar-laced “3 AM.”

The band has said the title of its latest is both a play on the Rolling Stones’ “Exile on Main Street” and an affable dig at their own success. Perhaps such humor signals a desire to start digging deeper.

The moments when they strayed from their formula were the most winning. “The Difference” achieved melancholy grace with a country twang, and “So Sad So Lonely” exuded cheeky exuberance. A ferocious cover of the Beatles’ “She Came in Through the Bathroom Window” and an ardent take on Cracker’s alt-rock classic “Low” revealed the power this band could achieve with riskier, more ambitious material.

Seven-time Grammy-winner Morissette made her career putting it all on the line with her raw, feminist anthems and unapologetically quirky personality. Her fierce hourlong set highlighted her immense vocal range and knack for radio rock anthems with substance. Backed by a five-piece band and looking like a rock star in black vinyl pants, Morissette delivered a kinetic performance, pacing the stage and whipping her hair during the theatrical opener “Uninvited” and fierce rocker “Eight Easy Steps.”

Giving a sneak peak of her upcoming album, “Flavors of Entanglement,” due later this year, she played pretty rocker “Underneath” and the throbbing, almost medieval-sounding “Moratorium.” The playful mood culminated in her vampy cover of the Black-Eyed Peas’ “My Humps,” delivered in a pink boa.

New Orleans-based alt rock quartet Mute Math made the most of its opening slot. A fiery set of taut, textured songs from the group’s 2007 major-label debut showed off a knack for neatly blending rock ferocity, proggy experimentalism and a reggae style reminiscent of the Police. The memorable finale found singer-keyboardist Paul Meany doing handstands on his keyboard as the band went wild.