Monday’s line outside the Sinclair foretold a rocking hot-ticket event like Harvard Square hasn’t seen since Dan Ackroyd called his buddies to the 1992 opening of the original House of Blues a few blocks away. For this night, the first in a diverse five-night music series presented by Converse Rubber Tracks Live, former Sinclair headliners Dinosaur Jr. was merely an opener act for the Replacements, the iconic ’80s Minneapolis garage-punks whose reunion trek has been mostly festival-size.

Yes, on the one hand, this should have been a bigger venue. Free tickets for the series (which continues with synth-pop headliners Passion Pit on Tuesday, speed-metal kings Slayer on Wednesday, Chance the Rapper on Thursday and the punk Descendants on Friday) were distributed by lottery, which left many fans empty-handed. Dozens of late-arriving winners with wristbands were even left on the sidewalk, waiting for people to leave to make room in the 525-capacity club.

Inside, the Sinclair was packed more than usual, partly to accommodate an extra soundboard and a security/photo pit. But once Dinosaur Jr. followed local band Young Leaves, with J. Mascis stoking his scuzzy guitar leads through the arc of three Marshall amp stacks behind him, the anticipation built for a special night.

Then the Replacements hit the small stage like Lone Rangers in black eyemasks and proceeded to blow off steam with scrappy rock ‘n’ roll made for rooms like the Sinclair. There were a few sloppy moments like an aborted song launch while singer/songwriter Paul Westerberg fumbled to light a cigarette. At another point, bassist Tommy Stinson, the band’s other original member, piped, “Finally got that one down. Thanks for shopping.” And the middle of the quartet’s 85-minute set wandered into blues that goofed on Whole Foods and a T. Rex cover spot where the ever-youthful David Minehan (from Boston’s own Neighborhoods) got to sing “20^th Century Boy” with aplomb while he and Westerberg ripped away on their guitars.

But mostly, the Replacements – now anchored by drummer Josh Freese — were tighter and more professional in their duties than during their famously drunken heyday. Westerberg was focused and intense in the chorus to “Anywhere’s Better than Here.” And the homestretch – with fans on the floor hopping with fists in the air to anthems “Can’t Hardly Wait,” “Bastards of the Young” and “Alex Chilton” – delivered a transcendent payoff.  “Are you satisfied?” Westerberg sang in an encore of “Unsatisfied,” and for the crowd, that answer had to be affirmative.

Just make sure if you’re going to another one of these Converse Rubber Tracks Live Boston shows (promoting Converse’s new global headquarters on the city’s waterfront), get in line early to ensure you don’t miss out.