Tsitsipa struck first with a break in the third game of the opening set, then saved three break points to lead 3-1. He then earned a double break for 4-1 and claimed the set as Ruud double-faulted after 36 minutes.
In the second set, Tsitsipas got out of trouble in a 13-minute game, saving three break points at 3-3 after leading 40-0.
He claimed the title three games later on a first match point, a forehand winner down the line.
He said afterwards that a chat with his team the night before the final gave him the spark he needed against his Norwegian opponent.
"I told them I would go out and play fearless tennis and that's what I did. I couldn't let the team down. I wanted to make the most of it," said the 25-year-old who had stunned Australian Open winner and world number two Jannik Sinner in the semi-finals.
"I showed some unbelievable, ruthless tennis."
He added that his 98-minute victory was more special than his first two title triumphs and cited a no-nonsense attitude heading onto the court.
"This is amazing, I want to thank family, friends and those who made this moment possible," he said. "(Completing) the trinity (hat-trick) is even more special than the first two."
"This match was nerve-wracking - I really wanted the trinity and I got it today. I played cohesive tennis from start to finish."
Ruud, twice a French Open runner-up, apologised to the capacity crowd for not being able to mount a consistent challenge to his Greek opponent.
"Congratulations to Stefanos for winning again, he's been playing so well all week," said 10th-ranked Ruud. "You are now back where you belong (among the top players)."
"I'm sorry I could not put on a better performance today. Hopefully, I will be back with a better performance in another year.
"I couldn't get it this time, but hopefully I'm getting closer to these big titles. I want to break the barrier and win a big tournament like this."
Tsitsipas produced 30 winners to the 20 of Ruud who had reached the final with victory over world number one Novak Djokovic on Saturday.
He is the fifth man to win three or more Monte Carlo titles, joining Rafael Nadal (11) and Bjorn Borg, Thomas Muster and Ilie Nastase, who all won three apiece.
