Martins struck in the 47th and 50th minutes to kill off the tie with his side leading 1-0 from the first leg.
However, substitute Indrek Zelinski pulled a goal back for the Estonian visitors with 25 minutes remaining to give them a glimmer of hope.
Goals from South African star Benni McCarthy and a long-range effort from from David Bentley helped Blackburn win only their second game in 18 European matches.
The result gave Rovers a 4-2 aggregate victory over Salzburg with the Austrian side's legendary coach Giovanni Trapattoni telling Blackburn boss Mark Hughes that the English side can win the trophy.
West Ham's woes continued when they were beaten 3-0 on the night, and 4-0 on aggregate, by Palermo in Sicily. Hearts drew 0-0 with Sparta Prague, but went out after they had lost the first leg 2-0.
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