Reni Maitua and Mitch Brown crossed in the first half for a 12-8 lead, Josh Walters replying for Rovers.
Matty Dawson, Micky Higham and Gareth Hock secured a 16th successive win for Leigh, although tries from Luke Briscoe and Kyle Briggs ensured a nervy finish.
Leigh and Leeds are the only two sides with maximum points in the Qualifiers.
After finishing top of the Championship, the Centurions have won their first three games since the start of the Super 8s as they bid to get back into the top flight for the first time since 2005.
Featherstone: Craven; Duckworth, Hardman, Taulapapa, Briscoe; Briggs, Thackeray; Griffin, Ellis, Baldwinson, Tagg, Walters, Spears.
Replacements: Day, Snitch, Cooper, Ormondroyd.
Leigh: McNally; Higson, Brown, Armstrong, Dawson; Ridyard, Drinkwater; Moimoi, Higham, Weston, Maitua, Paterson, Hock.
Replacements: Hood, Tickle, Hansen, Hopkins.
Referee: Jack Smith
Leigh Centurions edged closer to a return to Super League as they overcame Featherstone to maintain their 100% start to the Qualifiers.