Rhinos went ahead after only two minutes when Jack Ormondroyd sent fellow signing Cory Aston between the posts and Liam Sutcliffe, Leeds’ captain, added the extras.
Winger Marcus Webb, signed from South Wales, pulled a try back for the hosts before Handley scored his first, from a pass by Jimmy Keinhorst.
Two tries in four minutes either side of half-time edged Hunslet ahead. Jake Normington stormed over on the final play of the half, Joe Sanderson converting and then Joel Gibson touched down soon after the resumption.
Hunslet were close to extending their lead on 53 minutes, but Handley intercepted on his own line and raced the length of the field for a try which Sutcliffe converted.
Josh Walters’ try extended Rhinos’ advantage to six points, but there was no conversion and Hunslet came close to snatching a draw with ex-Leeds academy duo Nyle Flynn and Jack Norfolk both being held up over the line in the final moments before Jordan Lilley sealed it with a stoppage time drop goal.