It could have been an even more difficult game for Raith had Callum McGregor's early effort from the edge of the area not found the junction of debutant Josh Rae's right-hand post and crossbar.
Maeda was also denied before the interval by an offside flag after tapping home Anthony Ralston's cross.
With Bundesliga leaders Bayern Munich next up at Parkhead in the Champions League on Wednesday, the likes of Alastair Johnston, Cameron Carter-Vickers and Auston Trusty were given the night off.
As was goalkeeper Kasper Schmeichel, with Viljami Sinisalo making his Celtic debut.
There was no discernable drop-off in levels for Rodgers' men, who have now scored 14 goals in their last three games and 110 for the season as a whole.
It was a harsh lesson for Barry Robson's Raith, who thought they were heading in just one goal down at the interval before Maeda pounced for his second to remove any doubt about the outcome.
Celtic's quality shone throughout the second period and they can now look forward to the visit of Harry Kane and co on the back of another healthy victory.
The only downside is that man of the moment Maeda is suspended for the first leg.