The mercurial Australian, out of action since the Good Friday derby against Hull, outshone England hopeful Luke Gale as the Robins’ redemption victory lifted them above champions Leeds into 10th spot.
Kelly crossed for one of the visitors’ 11 tries - which included a hat-trick for centre Thomas Minns - and was directly involved with another five as Webster’s squad shrugged off the criticism caused by their home cup knock-out to Championship opposition.
Winger Ken Sio and centre Iain Thornley also grabbed doubles as Hull KR ended a run of six games without victory against Daryl Powell’s sloppy home side, who failed to score in the second half.
Rovers led 20-16 at half-time, outscoring their hosts four tries to three. Bidding for a first away win at the Jungle since February 2010, they made a perfect start, scoring with their first set from try line to try line.
Sio returned Gale’s kick-off with a 60-metre run to lay the platform for Maurice Blair to eventually bulldoze over from Iain Thornley’s off-load. Full-back Ben Cockayne, who finished with seven goals, landed a fine conversion.
Castleford, beaten last time out at Wigan, hit back through ex-Robin Jake Webster after 14 minutes. The 32-year-old centre, who signed a 12-month contract extension earlier this month, smashed through three would-be tacklers from Gale’s pass and Gale goaled to bring the Tigers level.
Ryan Hampshire’s first touchdown since his move from Wigan and another Gale conversion took Cas in front, only for Kelly to inspire Rovers’ response.
Minns, second-rower Graeme Horne and Kelly crossed in the space of 10 minutes, Cockayne added one conversion and the Robins were 20-12 in front - much to the delight of their coaching staff.
Castleford were not finished, however, and Australian winger Jy Hitchcox raced over in the corner to add to his hat-trick in his team’s previous home game against Huddersfield.
Kelly, though, was proving the difference between the teams at this stage and from the restart the Robins extended their advantage.
Kelly floated an angled kick and Minns jumped and collected with ease before touching down. Cockayne’s third goal was his best so far and the Tigers trailed 26-16.
Rovers continued to dictate terms and were good value as they turned the screw on the home side with further tries from Thornley, Mitch Allgood and Sio.
Castleford’s Paul McShane and Shaun Lunt of Hull KR were sin-binned for fighting and both sides put on a team warning for persistent offending.
However, it was fitting as impressive Rovers finished as they started, adding three tries in the last six minutes through Sio, Minns and Thornley.