John Mayer aligns with the Dead’s Bob Weir, Bill Kreutzmann and Mickey Hart.

Did you hear the one about John Mayer playing with the Grateful Dead gang? It’s no joke – particularly in light of the jam-iced envelopment of Dead & Company’s assured Tuesday show at Worcester’s sold-out DCU Center.

When all four survivors of the Grateful Dead regrouped to mark the band’s 50^th anniversary with Fare Thee Well concerts in Chicago this past July, the choice of Phish’s Trey Anastasio to tackle the high-pressure Jerry Garcia role seemed smart in terms of both the music and marketing. After all, Phish was the jam-band that took the Dead aesthetic to new heights of popularity and improvisational aplomb.

But beyond Chicago’s farewell assemblage, when guitarist/singer Bob Weir and drummers Bill Kreutzmann and Mickey Hart decided to take the show on the road without tour-wary bassist Phil Lesh, many fans shuddered at the news that pop dilettante John Mayer would succeed Anastasio in that fraught lead-guitar spot.

Of course, somewhere between singing “Your Body is a Wonderland” and dating Katy Perry, Mayer dug into gritty blues playing with Buddy Guy and Eric Clapton. And low and behold, the Berklee-schooled guy did his homework and fits right in with the so-called Dead & Company. Not only does he nail the guitar tone and phrasing to cover those Garcia parts, but Mayer’s a more solid lead singer than Weir or Anastasio or especially Lesh, so the new band can roll through the songbook without technical glitches.

Also, whether it’s a matter of more rehearsal or chemistry, Dead & Company proved more crisp and confident in Worcester than the uneven Fare Thee Well crew, with Hart stepping up to balance the double-drums tandem.

After Mayer went toe-to-toe with Weir on a spiraling “Cassidy” opener, however, Tuesday’s first set slid into a dull run of down-tempo tunes. Mayer stirred “Row Jimmy” with his slow blues licks, but didn’t need a chicken-neck head bop to kick into “Ramble On Rose,” and after a slightly peppier “Big River,” the set dipped further with “Peggy-O” before Mayer hit the stock throttle to build “Sugaree.”

But like many a Dead (or Phish) concert, a song-based first set usually leads to a more inspired, segue-heavy second set. And Tuesday’s proved the saving grace, with Mayer soon morphing into an elastic string of “Uncle John’s Band,” “Estimated Prophet” and a sublime “Terrapin Station” capped by percussive crescendos.

Yet it was bassist Oteil Burbridge (Allman Brothers, Tedeschi Trucks Band) who emerged as Dead & Company’s secret weapon, holding down Lesh’s spot while Fare Thee Well carryover Jeff Chimenti covered the keyboards. Burbridge’s percolating notes jazzed up the band’s interplay of spidery string work, and he animated the reggae-tinged “Estimated Prophet” when he pointed and laughed at a man in the far balcony who was costumed as a stick figure in glow sticks. While Mayer and Weir traded lead vocals, Oteil also sang high harmonies. And during the drummers’ Rhythm Devils spotlight, the bassist dealt the night’s biggest surprise, taking a turn behind Kruetzmann’s kit to power a jamtronica-flavored jam while the percussionists pounded kettle-sized drums.

Dead shows could peter out post-drums, but that didn’t happen Tuesday, thanks to a pair of perfect covers that were part of the Jerry Garcia Band’s repertoire. A brief space jam (where Mayer showed that he can noodle with the best of them) drifted into the Beatles’ “Dear Prudence,” done proud by Weir on lead vocals before Mayer sang the groovy boogie “Get Out of My Life, Woman” in apparent honor of its New Orleans author Allen Toussaint, who just died on tour in Spain at age 77. From there, a chugging “Going Down the Road Feeling Bad” and the celebratory encore “Ripple” (with Mayer on acoustic) sent the grateful crowd home after three-plus hours.

Other bands are out recreating and recasting the Dead catalog, including the Dark Star Orchestra (which plays House of Blues on Nov. 18) and Further drummer Joe Russo’s Almost Dead, which plays the Paradise Rock Club on Nov. 27-28. But with John Mayer acting like a pro who could handle the demands of any tribute band, Dead & Company quickly and effectively have that covered at the arena level, the only group that still boasts three actual members from the Grateful Dead.