He was given the reprimand by Ramos but, because it was his first offence of the match, Cilic was issued with a warning and no points were deducted.
The US team, however, fought back on Saturday as the duo of Mike Bryan and Ryan Harrison earned a dramatic five-set win over the Croatia's Ivan Dodig and Mate Pavic. The Americans remained calm and they won the next three points to steal another set and move two sets to love up.
Coric rallied from two sets to one down to beat Frances Tiafoe 6-7 (0), 6-1, 6-7 (11), 6-1, 6-3 in the fifth and decisive match.
The French, who defeated Spain 3-2 in the other semi-final in Lille, will have home advantage in the November showdown and hope to avenge their 3-2 loss to the Croatians in the 2016 semi-final.
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Yet with everything resting on the first duel between two of tennis's brightest young "Next Gen" men, Coric overcame the loss of two very contrasting tiebreaks to book Croatia's final date against champions France.
However, there were no controversies for him to deal with yesterday as Cilic beat Tiafoe 6-1, 6-3, 7-6 (7-5).
Both Cilic and Coric had won their singles matches on Friday, before the USA cut Croatia's lead to 2-1 as Mike Bryan and Ryan Harrison beat Ivan Dodig and Mate Pavic in a dramatic doubles rubber on Saturday.
Cilic couldn't recall the last time he had smashed a racket.
Croatia secured their place in the Davis Cup final with a 3-2 victory over the US in Zadar.
There was further frustration for Coric, who led 5-1 in the third set which he eventually lost on a lengthy tie-break.
"I didn't know Ramos was sitting in the chair".
Thiem and Novak won the singles on Friday to give the hosts a 2-0 lead, but Australia captain Lleyton Hewitt teamed with John Peers to win the doubles rubber the following day and keep the tie open.