Two decades ago, Matthew Sweet filtered his wide-ranging emotional response to his divorce through his twin obsessions with Neil Young and the Beatles and produced a power-pop masterpiece. Tuesday night, he brought it to the Paradise, commemorating the 20th anniversary of “Girlfriend” by playing the album in its entirety. To the surprise of nobody in attendance, it turns out to hold up awfully well.

Sweet and his three-man backing band opted to honor “Girlfriend” without being slavishly beholden to duplicating its exact sound. Not that the thought didn’t cross Sweet’s mind; he casually mentioned his idea to find a turntable to re-create the vinyl outgroove sounds added to the CD to signify the end of each “side.”

But Sweet was largely happy to play a noisy, freewheeling rock show unconcerned with the record’s Beatlesque production flourishes. It got him into trouble on rare occasions – a dramatically sped-up “Don’t Go” quashed the song’s darkly psychedelic pop in favor of punkish aggression, and “Thought I Knew You” seemed oddly unformed. (The mix remaining unresolved until midway through opener “Divine Intervention” caused its own frustrations.)

Despite those exceptions, the songs sparkled, in sometimes surprising ways. “Looking at the Sun” emphasized a borderline-funky chop, and the lack of acoustic guitars enhanced the previously underplayed Neil Young hack driving “Winona.” On “You Don’t Love Me,” Sweet’s saddest song became more ramshackle but also more defiantly epic.

Tasked with an unenviable job, guitarist Dennis Taylor played exactly enough of Richard Lloyd’s and Robert Quine’s effervescently inventive original leads to sound right and then took off on his own. Longtime Sweet cohort Ric Menck, meanwhile, was nondemonstrative (as ever) while drumming up a storm (as ever), fueling the rolling slashes in the album’s title track. “Then, we were young and strong/ Now, everything is wrong,” sang Sweet in his still-creamy voice on “Time Capsule,” one of a handful of post- “Girlfriend” encore songs. Certainly, he proved the first part was true.

Openers A Fragile Tomorrow played with a rootsy denseness on songs that were tuneful but spark-free.