Scrum-half De Klerk, a World Cup winner for South Africa last year, darted over for the game's decisive try three minutes from the end at the AJ Bell Stadium in Salford as Sale clinched their first trophy since 2006.
Sharks' last trophy triumph came 14 years ago when they won the Premiership title, while Quins, who played their full part in a nerve-jangling final, were denied their first silverware since their Anglo-Welsh Cup success in 2013.
Curtis Langdon's converted touchdown and Du Preez's penalty had given Sale a head start, but Smith's 50th-minute penalty put Quins 19-10 ahead.
Sale back row Dan du Preez's 66th-minute touchdown and brother Rob's conversion hauled their side to within two points of their opponents.
Rob du Preez's 75th-minute penalty edged Sale ahead and De Klerk's late effort, which Rob du Preez converted, put the result beyond doubt.