The Toffees dominated the opening 45 minutes of the Merseyside clash and they were rewarded in just the 16th minute, when Pienaar tucked Seamus Coleman's low cross home from eight yards after some superb build-up from the hosts.
Everton began the day six points off fourth-placed Chelsea and although they closed that to three the Stamford Bridge side have a match in hand. Significantly, however, fifth-placed Spurs drew at Wigan, meaning their cushion over the Merseysiders is now only three points.
Marouane Fellaini's early header was saved by goalkeeper Mark Schwarzer before they took a 16th-minute lead, having assumed control of the game without so much as a word of objection from the visitors.
The Toffees had enjoyed plenty of penetration down the right and it was no surprise when Kevin Mirallas and Leon Osman combined to play in Coleman close to the byline for him to cut the ball back to the penalty spot where Pienaar ran in unchallenged to side-foot home.
Victor Anichebe looped a long-range header wide as the Cottagers continued to show little intent, then they were handed a blow when Dimitar Berbatov limped off after half an hour, with Mladen Petric stepping in.
Fellaini had Everton's two best chances before half-time, curling one effort wide after neat interplay by Pienaar and Nikica Jelavic, before team-mate Anichebe blocked his goalbound effort.
In between those Jelavic, a shadow of his prolific self of 12 months ago, could not decide whether to shoot or cross to Anichebe having been sent clear by Coleman and ultimately screwed the ball across goal and embarrassingly out for a throw-in.
Fulham's first chance came just before the break when Kieran Richardson's cross rolled just out of the reach of Petric at the far post.
They improved in the second half and Urby Emanuelson should have hit the target from Alex Kacaniklic's cross 10 minutes after the interval.
Mirallas' tumble in the area had the Belgium international appealing for a penalty but despite contact from Stanislav Manolev the Everton forward was already falling over. The Belgian's next intervention was brilliant, however, flicking it over Manolev before hitting a volley which Schwarzer palmed away.
Anichebe then looped a header just wide of the far post as Everton finally regained the dominance they had enjoyed in the first half.
Fellaini would have wrapped up victory five minutes from time but somehow bundled over Leighton Baines' cross from close range while substitute Ross Barkley forced a good save from Schwarzer when put clean through in added time.