Yesterday in the TT final, the West Indies needed 19 in the final over and pulled it off. What is the record for this in different formats; TT, ODI, domestic etc. ?

Also what is the record in a major international final? I certainly can't remember one where more than 19 was successfully chased.

Most runs scored in the last over to win in a World Cup match - Latest Cricket News, Articles & Videos at CricketCountry.com
This article looks at World Cup games and the record is 14 by Pakistan against WI in 87; IIRC Abdul Qadir hit the runs and Walsh famously chose not to run out a batsman at the bowler's end.