Raja and Sharan took one hour 23 minutes to register the win on their fourth match point at the Olympic tennis School Tennis Complex.
The Indian pair led 6-2 in the Super Tiebreak before the Israelis clawed their way back.
Despite serving two double faults and missing three match points, Raja and Sharan played some fine tennis in the end to wrap up the match.
In the first set, the Indian pair was broken in the 12th game but came back solidly in the second set to break Weintraub's serve in the seventh game and Sela's serve in the ninth game to win the second set.
The Indian pair will take on Russian pair of Mikhail Elgin and Teymuraz Gabashvili in the doubles finals tomorrow. The Russians scored a 6-3 5-7 10-4 win over James Cerretani of USA and Adil Shamasdin of Canada in the other semifinals.
Divij Sharan-Purav Raja in final of Tashkent Challenger
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