Saha's 203 and skipper Cheteshwar Pujara's unbeaten 116 helped Rest of India overhaul the target with six wickets still in hand.
Wicketkeeper Saha and Pujara, unbeaten on 123 and 83 respectively last evening in a team score of 266 for four, carried on in imperious fashion on the fifth and final morning to steer the team home an hour before lunch in 19.1 overs at the Brabourne Stadium here.
Rest of India finished with 379 for four in 103.1 overs to cruise home in style.
The duo's fifth wicket unbroken partnership was worth 316 runs in 78.5 overs. It was the second-best in the tournament's history after the highest of 327 for the fourth wicket between Ravi Shastri and Praveen Amre for Mumbai against the Rest at Bengaluru in 1990-91.
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Both the batsmen were largely untroubled by the newly crowned Ranji Trophy champions' bowling attack even though the target set by Gujarat, who had taken a handy 132-run first innings lead, was stiff.
Saha's unconquered effort, after he reached his first-ever double century with a four off Karan Patel, lasted 346 minutes and 272 balls. It was also the highest score by a wicketkeeper batsman in the tournament's history.
The Bengal and India stumper struck 6 sixes and 26 fours in this important knock that has come before the selectors sit down to choose the Test team for the one-off game against Bangladesh in Hyderabad next month.
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Rest had more or less ensured victory last evening itself as they needed 113 runs with Pujara and Saha, who counter-attacked the bowling with gusto when his team was in deep trouble at 63 for four, firmly entrenched.
The duo sailed along merrily on the fourth morning with Pujara duly compiling his 6th hundred of the first class season, including three in Tests, and 37th overall before Saha went past his previous career-best score of 178 made in the Ranji Trophy against Assam seven years ago in Kolkata with a couple to square leg.
The limited Gujarat bowling resources were ruthlessly exposed by the two batsmen in the second innings after they had bundled out Rest for a measly 226 in the first.
Left arm spinner Hardik Patel was the most successful bowler with figures of 2 for 104 while the other two wickets were shared by medium pacer Mohit Thadani and off spinner Karan Patel.
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Pujara later praised Saha's knock and said when the two joined forces it was the wicket keeper batsman who told him he was going after the bowlers to which he concurred and the match-winning triple century partnership ensued.
"We needed someone to take on the bowlers and unsettle them, (and) that's what he started doing. At the other end I was there to hold up the innings, playing the ball on merit. Things did work out for us. We had the proper plan when we lost four wickets," he added.
"To chase 370 was not easy, (especially) when you lose four wickets early on and the bowlers are on top. At one stage I felt we probably will lose this game. When Wridhi came in, the way he was hitting the ball, I also got lot of confidence.
"After a couple of overs he felt he had to take on the bowlers and even I felt the same. We wanted to unsettle their line and length, they don't have pace - only medium pace - and both of us have faced fast bowlers at 140 km an hour. To counter them we had to come up with a plan. Wridhi came up with that and I supported him.
"This is one of the best knocks of his. He has scored hundreds at international level. It was one of the best innings I have seen in domestic cricket."
He also praised the track.
"It was a very good wicket. There was something for fast bowlers right through and day three onwards there was something for spinners (too). It was a very sporting wicket.