Coleman ignited a hitherto drab Barclays Premier League affair at Goodison Park with a well-placed header 10 minutes before the break.
Former Fulham striker Saha doubled the Toffees' lead from a free-kick early in the second half but a Clint Dempsey strike prevented the home side easing to victory.
Defeat could have been heavier had Carlos Salcido not produced a fine headed clearance off the line from Phil Jagielka late on.
Everton were always the dominant side and fully deserved to repeat their victory over the Cottagers in Moyes' first match just over nine years ago.
The downside was the loss of Saha, who was playing for Fulham in 2002, on a stretcher in the closing minutes.
Source: PA
Source: PA