"It feels great", world No 15 Tsitsipas said.
"I've spoken to him (Hewitt) every day, after every match, he sends me a message and we sort of have a little bit of a chat".
Rublev has maintained his form to advance to the semi-finals with win over Italian wild card Liam Caruana 4-3 (7), 4-1, 4-2 on Thursday.
The young Greek star, and number one seed, completed a ideal run through the tournament with a 2-4, 4-1, 4-3 (3), 4-3 (3) victory over the 19-year-old de Minaur. The match was hanging at 4-3 (7/3), 3-4 (5/7), 4-0, 2-4 by then and Tsitsipas was understandably frustrated by the injury. It was a fantastic match, I stayed calm. "I was mentally very strong and that was proven in the tie-break in the last set". He was also named ATP's Most Improved Player.
The Australian began the season at number 208 and reached a career-high 31 last month. Tsitsipas made no mistake on his third, though, after the Australian sent a forehand long. "I never expected nearly anything that happened this year", said the player from Sydney. "All credit to Stefanos".
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"One of the main things that I always loved about the sport is the individual aspect, just being you on court and you having to find a way to deal with situations".
He added: "And I'm very happy it's over".
The 20-year-old Tsitsipas, who had medical treatment on his left hand during the fourth set, had only dropped one of 30 service games in the tournament prior to the semifinal but was broken three times by Rublev.
The format for the tournament is the best-of-five sets with shorter sets of four games, no-ad scoring at deuce and no lets on serve.