The American, who warned the Portuguese that he would never again umpire one of her matches, went on to lose in straight sets to Naomi Osaka and later accused Ramos of treating her more harshly than would have been the case had she been a man.
Cilic and Coric both won the opening rubbers in straight sets to put Croatia in a strong position after the opening day.
Earlier, Cilic wasted a 6-1 lead in the second-set tiebreaker then completely fell apart with a series of errors under pressure from the big-serving Querrey.More news: Kansas City McDonald's workers to join nationwide protest on sexual harassment
Albert Ramos Vinolas beat Richard Gasquet 1-6 6-4 14-12 before Marcel Granollers edged Mahut 6-7 (7-2) 6-3 13-11.
Croatia set their target at the second title of the tournament, with their only previous winning experience in 2005.More news: Renault-Nissan-M'bishi alliance ties up with Google on in-car services
Down 2-0 after singles play, Bryan, the world's No. 1 doubles player, and Harrison outlasted Ivan Dodig and Mate Pavic 7-5, 7-6 (6), 1-6, 6-7 (5), 7-6 (5) in a match that lasted almost five hours.
Cilic couldn't recall the last time he had smashed a racket.
There was further frustration for Coric, who led 5-1 in the third set which he eventually lost on a lengthy tie-break. "This is the best tennis I've seen from my team in three years", French captain Yannick Noah said.
In Lille there was relief that the Croatians had won as it guaranteed the final would be a home tie for France.More news: Hailey Baldwin and Justin Bieber are definitely married: Alec Baldwin
In World Group Playoffs action past powerhouses Australia and Switzerland were upset, leaving their status in limbo as the ITF prepares to announce which teams will participate in next year's restructured Davis Cup.