The World Cup-style event between MLS and Liga MX Mexican squads had three-team groups from which two clubs advanced to the knockout stage.
After an earlier loss, Nashville had to beat the host Revolution by two goals to advance on goal difference, with Mazatlan's fate awaiting the outcome.
US striker Bobby Wood put the Revolution ahead in the third minute but Nashville goals leader Sam Surridge equalized in the first minute of first-half stoppage time. The English forward ended a Nashville scoring drought of 386 minutes to make it 1-1 at the break.
A scoreless second half between the clubs with the fewest goals in MLS this season ensured New England would advance to a knockout opener against New York City and send Mazatlan into a knockout start against DC United even before the Revolution won 5-4 on penalties.
Nashville, which fell to Inter Miami in the 2023 inaugural final, was sent packing before the 32-team knockout phase.
Inter Miami will host a knockout opener on Thursday against Toronto with the winner to face either Sporting Kansas City or reigning MLS champion Columbus Crew in round two.
Other opening matches in that quarter include Tigres against Pachuca and New York City against New England.
Other openers on that half of the knockout bracket include Cincinnati against Santos Laguna, Montreal against Philadelphia, Orlando City against Cruz Azul and DC United against Mazatlan.
Reigning Liga MX champion Club America opens knockout play against Mexican rival Atlas with the winner to face Portland or St. Louis in the second round.
Other first-round matchups in that draw quarter include Houston against Toluca and Colorado against Juarez.
Other opening matches in that half of the draw include Seattle against the Los Angeles Galaxy, Pumas versus Vancouver, Los Angeles FC against Austin and San Jose against Necaxa.
