Thursday at the Square ended its soggy summer run on a Southern note with young bluegrass phenoms the Avett Brothers. It was a high note for the series, especially after the low point last week when storms forced a rare cancellation.

The Avetts — siblings Scott on banjo, Seth on guitar, and Bob Crawford on bass and Joe Kwon on cello—opened boldly with “Distraction #74” from 2006’s “Four Thieves Gone” — a shambling jam born of the Carolina hills. From the first note, the Square’s pit and edges were packed with fans who clearly have the Avetts on their radar. The band followed with “Shame” from 2007’s magnificent “Emotionalism.”

That whole special album features early-Beatles harmonies (think “From Me To You”) filtered through a roots Americana lens. For example, “Will You Return?” is about a relationship that ended on a hopeless note. Scott Avett sings about awkwardly stuttering through a goodbye and then actually does it, “Oh m-m-my, Goodb-b-bye.” It’s little nuances like this that have turned the Avetts into contemporary songwriters that matter.

The jamboree atmosphere really took off with “The Perfect Space,” which added a touch of Lynyrd Skynyrd. The line “I wanna have pride like my mother has/And not like the kind in the Bible that turns you bad” made people stop and take notice. Then the crowd tossed colored plastic balls in the air, turning the Square into a kids’ play pit.

The Avetts have a reputation for astounding live shows, and expectations were exceeded. The band gives its shows an intimate backyard barbecue feel. Indeed, check out the YouTube video where they sing “Will You Return?” in the back of a jam-packed tour bus.

The band’s new album (produced by the legendary Rick Rubin) “I and Love and You” comes out in late September. Judging by the cuts “Laundry Room” and the title track (both offered Thursday), its major label debut for Columbia should be the band’s breakout album.

Midway through its set, the band played “The Salvation Song,” which had a Tammy Wynette feel, believe it or not. Crystal- clear vocals on “Matrimony” and “I Would Be Sad” helped convey the songs’ honest messages.

Chicago bluegrass group Cornmeal opened and its entire set was phenomenal. Its enthusiastic cover of Paul Simon’s “I Know What I Know” really put it over the top. If the dive bar Bob’s Country Bunker, from “The Blues Brothers,” was real, Cornmeal would be on stage and the Avetts would be on the jukebox. Both groups would go down well with such a crowd.

The Avetts were the perfect sendoff for this year’s installment of the free outdoor concert series. But Buffalo Place Rocks the Harbor continues Saturday with Bruce Hornsby & the Noisemakers, Sunday with Gov’t Mule, Sept. 4 with The Wallflowers and Sept. 5 with Great Big Sea.

That Buffalo Place would book an up-and-coming band generating a lot of buzz such as the Avett Brothers shows that the organization knows talent when it sees it. What was undoubtedly a frustrating few months weather-wise for organizers and fans alike ended on a bright note.