Everton managed to hold off a second half serge from Stoke City and walk away with three points in a game that should have been dead and buried at half time.
Two early strikes from Jo and Lescott had the Blues cruising and looking like notching up a cricket score having had no efforts to save from Tony Pulis' men.
But a Ryan Shawcross goal just after the break brought a nervy second 45 for the Blues who managed to bag a third in added time to produce a scoreline that slightly flattered their performance.
Unbeaten now in eight, the home started the brighter with Pienaar and Baines allowed to repeatedly charging down the left and the pair had linked up well to carve open the Stoke defence inside the first five minutes but a well timed tackle from Andy Wilkinson stopped Pienaar from pulling trigger from seven yards.
The Blues continued with the pressure and a minute later Baines quick footed his way to the byline and found Osman but a similar tackle from Higginbotham was enough to keep the scores level.
Despite former Everton striker James Beattie being in the form of his life it was David Moyes' men who looked the most threatening and with only 17 minutes gone they deservedly found the opener.
A long punt up field was easily won by Jo to play in Fellaini who with his first touch sent it back to the Brazilian who strode into the box and drilled it low beneath Thomas Sorensen who almost dropped in time to block the shot but the ball squirmed over the line.
Having won every high ball hoisted forward, partners Beattie and Sidibe couldn't manage to latch on to any second balls and never troubled the organised Everton defence.
The home side were making all the running pinning Stoke deep inside their own half and marking his 100th appearance for Everton Lescott marked his mile stone with his side's second of the game.
Under no pressure to hurry the ball Osman was allowed to control and pick his cross from the edge of the area and Cahill rose to sting the palms of Sorensen with a strong header but while still picking himself off the deck the keeper could do nothing to stop Lescott steaming in at the back post for the easy tap in.
Unlucky not to have found a third minutes before the break Everton were spreading the ball about like a training exercise when Jo found himself running at the red and white back line and a neat ball to the feet of Osman brought a clever turn and curling effort which flew inches wide.
Having failed to get a single shot on target in the first half, Stoke looked to be in for a rout with the introduction of Louis Saha for the Toffees but they forced their way back into the game on 52 minutes through Ryan Shawcross.
An in-swinging corner from Liam Lawrence was not attacked by a Blue shirt and Shawcross raised head and shoulders above all surrounding and powered his header past a scrambling Tim Howard.
Replenished by the goal Stoke were throwing bodies forward and it was Shawcross again who could have brought the scores level minutes later after another corner wasn't cleared and Higginbotham's header bounced inches from his outstretched boot.
The introduction of Ricardo Fuller only troubled the Blue defence even further and after winning a knock down to Salif Diao his blast was blocked by a last second lunge from Lescott.
Everton still looked a threat on the break and Jagielka whipped a ball into the near post but the keeper missed his punch fooling Saha who was closing in behind him.
Sorensen kept his side in the game on 73 minutes with a double save from Jo, once at the feet of the goalscorer and then his attempted curling rebound much to the appreciation of his team mates.
With only four minutes on the clock Everton broke after substitute Jack Rodwell won the ball and through Fellaini Osman was and released and surged forward before drilling it at Sorensen but after dangerously spilling the ball at the feet of Saha the keeper recovered to save the Frenchman's rebound with his body.
The game was put out of Stokes reach in added time when Baines launched a high ball to Fellaini who guided the ball down from over his shoulder with his right and slotted home with his left in what was the move of the game.
After the match Everton boss David Moyes said: "We were very comfortable in the first half but they worried us after the break.
"We didn't start the second half great and they had corners and crosses raining in which unnerved us a little.
"Cahill came off with a slight calf strain and we missed him but the lads did well.
"it is very tight at the bottom and every point to the lower clubs are vital so these games are never easy.
"Thankfully we hung in there and I'll take the win anyday.
"There are nine games left and we have to win most of them if we are to catch the teams above us but we are playing well and on a bit of a run and hopefully it will continue.
Tony Pulis said: "Tony Pulis said: "I was very disappointed with the first half.
ÃÂâÃÂÃÂÃÂÃÂWe didn't throw any punches and we gave them all the initiative.
ÃÂâÃÂÃÂÃÂÃÂFor 25 minutes in the second half we had them hanging on and we didn't deserve the third goal.
ÃÂâÃÂÃÂÃÂÃÂIt was very soft and you cannot come to places like this and give them sort of goals away.
ÃÂâÃÂÃÂÃÂÃÂThere are still nine games to go, five at home, so our destiny is clearly in our hands and we have a great chance of staying up.
ÃÂâÃÂÃÂÃÂÃÂWe just need to approach the rest of the games like we did the second half today.ÃÂâÃÂÃÂÃÂÃÂ
Teams.
Everton: 24 Tim Howard, 3 Leighton Baines, 4 Joseph Yobo, 5 Joleon Lescott, 6 Phil Jagielka, 11 Jo, 17 Tim Cahill, 18 Phil Neville, 20 Steven Pienaar, 21 Leon Osman, 25 Marouane Fellaini
Subs: 1 Carlo Nash, 8 Segundo Castillo, 9 Louis Saha, 15 Lars Jacobson, 26 Jack Rodwell, 32 Dan Gosling, 38 James Wallace
Stoke: 29 Thomas Sorensen, 3 Danny Higginbotham, 6 Glenn Whelan, 7 Liam Lawrence, 11 Mamady Sidibe, 17 Ryan Shawcross, 18 Salif Diao, 20 James Beattie, 24 Rory Delap, 25 Abdoulaye Faye, 28 Andy Wilkinson
Subs: 1 Steve Simonsen, 10 Ricardo Fuller, 14 Danny Pugh, 19 Amdy Faye, 26 Matthew Etherington, 27 Henri Camara, 33 Ibrahima Sonko
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