The lanky left-hander opened the innings with Sachin Tendulkar (23 in 23 balls) who was playing only his second game of the tournament after being ruled out to due to finger injury.
They put on a half-century stand for the first wicket and then added a quick-fire 75 runs in just 36 balls with Dinesh Karthik (35 in 20 balls) to pave the way for a fighting score.
Franklin, in his 13th game for MI, bettered his previous highest score of 45 not out scored against the Kolkata Knight Riders last season, struck four huge sixes and six fours after a nervous start.
The home team, seeking their fourth win in six games after having lost the earlier one at this venue comprehensively to the Delhi Daredevils, added only 34 runs in the last five overs after having added 71 between overs 11 and 15 when Frankling and Karthik went after the bowling.
MI got off to a sedate start before stepping up the pace in the rest the power play period of six overs to make 39 for no loss.
The first over from Praveen Kumar was a maiden to James Franklin, promoted in the order to accompany Sachin Tendulkar after the flop show by the other combinations tried out in the previous four games. Kumar also beat the tall left-handed batsman five times in six balls.
Left-arm spinner Bhargav Bhatt also kept the batsman under wraps before Tendulkar flicked Kumar in the third over for the first boundary. PTI SSR KHS