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Morkel contributed an unbeaten 40, including three fours and two sixes, to help Titans reach 178-5 off 20 overs at SuperSport Park and he took 3-26 as Lions fell just short at 171-6 in reply.
Victory lifted defending champions Titans two places to second, seven points behind Lions with two rounds left. The table toppers automatically qualify for the final and the second and third teams play off for the other place.
Lions have 25 points and only a dramatic collapse would deny them first place while Titans (18), Knights (17) and Warriors (16) are the main challengers for the two play-off places.
Titan Henry Davids atoned for the cheap exit of fellow opener Jacques Rudolph (6) by posting a 50 laced with three fours and four sixes while Pakistani Sohail Tanvir (2-26) and Aaron Phangiso (2-36) bowled best for Lions.
Quinton de Kock hit six fours and four sixes in his 73 to lead the Lions run chase but he, opening partner Themba Bavuma (17) and captain Alviro Petersen (0) all fell victim the the right-arm fast medium bowling of Morkel.