Leigh were missing Super League’s record try-scorer Josh Charnley and stand-off Lachlan Lam through knee injuries and badly missed their attacking prowess and influence.
They fell behind after 10 minutes when Burgess touched down in the left corner after good approach play from the home side.
Hiku quickly added to the lead when he dotted down Tyrone May’s clever kick through.
Alick-Wiencke showed good effort to get the ball down on the line to get Leigh back into the game.
Mikey Lewis had a drop-goal attempt come back off the post in the final moments of the half as the first 40 ended in mildly chaotic fashion.
Burgess was then forced off just after the restart after a tackle by Aaron Pene but the home side scored on their next attack after a clever kick from Lewis was passed inside to Whitbread.
The visitors will have been massively disappointed with their defence for Leyland’s try as he picked the ball up from dummy half and managed to ground the ball despite the attentions of three defenders
Hodgson reduced the arrears with 10 minutes to go but there was no real chance of a late fightback and Rhyse Martin’s late penalty for the hosts completed the scoring.
The Robins will now travel to Super League leaders Leeds next Friday, 26 June, and looking to avenge the thumping 58-6 defeat they suffered to the Rhinos in Las Vegas in March. Leigh visit Toulouse on the following day.
Hull KR: Broadbent, Davies, Hiku, Martin, Burgess, Lewis, May, Sue, Lawton, Amone, Hadley, Batchelor, Minchella.
Interchanges: Luckley, Whitbread, Leyland, Pangai Junior.
Leigh: Armstrong, Senior, Niu, Hanley, Hodgson, Cook, O’Brien, Ofahengaue, Ipape, Mulhern, Halton, Alick-Wiencke, Liu.
Interchanges: Brogan, Pene, Davis, Horne.
Referee: Chris Kendall.