ZZ Top and a Las Vegas residency go together like cheap sunglasses and classic Fords such as the iconic “Eliminator” hot rod, the namesake of the 1983 album that turned the Texas trio into a worldwide phenomenon. It’s hard to imagine ZZ Top’s career skyrocketing as high as it did if Billy Gibbons, Dusty Hill and Frank Beard didn’t play second fiddle to the talismanic candy apple vehicle featured in videos for “Legs,” “Gimme All Your Lovin’” and “Sharp Dressed Man.” They did, now here they are nearly four decades later, playing those songs in their third extended engagement at The Venetian Resort.

Gibbons, who has been known to use filed-down pesos for guitar picks, is the undisputed master of pinch harmonics as he expressively demonstrates in 1973 hit “La Grange.” The band encored with that song the last time they made Vegas their home on the range, along with “Tush” and “Jailhouse Rock,” while opening with hard-driving “Got Me Under Pressure.” Gibbons adds some squealing licks to the latter but it’s a good example of his penchant for double-stop riffing that surfaces again and again in ZZ Top’s repertoire.

The thing that makes Gibbons’ playing entirely his own is his laid-back style. It gives the songs a laconic feel, although the technique behind it is anything but. It’s hard to think of that sound without picturing the bearded, prospector-looking guy who has hardly ever been photographed without wearing shades, a testament to some canny marketing decisions that made ZZ Top ubiquitous on MTV during the music channel’s formative years. Videos aren’t as important now, but the blues-based boogie he creates with Hill and Beard, that borrows equally from Muddy Waters and Chuck Berry, is still as iconic as the coupe that drove them to superstardom.

The Venetian, 8 p.m. March 20-21, 25 & 27-28, starting at $49.95 plus tax and fee. 702.414.9000