After scoring 64 off 51 balls with the bat, Croft removed Tom Lewis and Brendon McCullum in successive balls before removing Laurie Evans with a one-handed catch as the Bears were bowled out for 137 runs with the penultimate ball of the match.
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After winning the toss, the Bears soon made inroads into the Lancashire batting lineup, with the top four batsmen all being removed during the early stages to leave the score on 34-4 after 7.1 overs.
However, Croft rescued his side with a knock of 64, hitting six fours and three maximums before ending the innings unbeaten.
Birmingham's reply began with McCullum hitting two sixes to immediately get his side above the run-rate, but fellow opener Varun Chopra could only make eight.
McCullum and Lewis took the attack to the Lancashire bowlers but they both fell in successive balls to Croft, with Lewis departing for 22 and McCullum for 41 off 25 deliveries.
The Bears still had the upper hand but Evans (13) and Ateeq Javid (18) fell to Faulkner, while Rikki Clarke (9) and Tim Ambrose (11) also fell cheaply to leave the home side still needing 23 runs with nine balls remaining.
Oliver Hannon-Dalby made things interesting with a six in the last over, but after he was caught off the penultimate ball, Lancashire could celebrate a vital win which strengthens their bid for a place in the quarter-finals.