A Kallum Watkins try and two Liam Sutcliffe goals forged an eight-point lead for the home side at half-time.
Hull KR, who started the Qualifiers by thrashing Batley, pulled level at 8-8 after James Greenwood's score.
But two tries from Leeds hooker James Segeyaro secured victory, the second after James Donaldson had gone over for the visitors to ensure a nervy finish.
George Lawler touched down in the final minute for Rovers, but they were unable to deny the 2015 Super League champions a fifth successive win.
Papua New Guinea-born Segeyaro is yet to be on the losing side since his move to the Rhinos from Penrith Panthers in July.
Leeds: Sutcliffe; Briscoe, Watkins, Moon, Hall; McGuire, Burrow; Galloway, Segeyaro, Singleton, Ferres, Ablett, Jones-Buchanan.
Replacements: Keinhorst, Achurch, Garbutt, Cuthbertson.
Hull KR: Cockayne; Sio, Minns, Thornley, Mantellato; Blair, Kelly; Tilse, Lunt, Allgood, Greenwood, Clarkson, Donaldson.
Replacements: Larroyer, Walker, Thompson, Lawler.
Referee: Phil Bentham
Leeds Rhinos made it two wins from two in the Qualifiers with a narrow victory over Hull KR at Headingley.