Kevin Mirallas scored a terrific solo goal as Everton condemned Stoke City to a sixth straight away defeat in the Premier League.
There appeared little danger when the Belgian midfielder collected the ball in his own half after Tim Howard had punched away a Stoke free-kick, but Mirallas had other ideas.
He managed to give Steven N'Zonzi the slip before turning the backtracking Geoff Cameron inside out and lifting the ball beyond Asmir Begovic on 27 minutes as the goalkeeper sped off his line.
Stoke had chances in the second period to rescue a point, but could not come up with the equaliser they needed to ease their own concerns as they continue to hover above the relegation spots.
Tony Pulis's side are 13th in the table with 34 points from 31 games, but have played one game more than 17th-placed Wigan and Aston Villa in 18th spot, who are both on 30 points from their 30 games.
Everton have no such concerns, and remain well in the frame for a European spot.
David Moyes's men are sixth in the table, but are only six points behind third-placed Tottenham with Arsenal two points clear of them in fifth spot and Chelsea four points above them in fourth spot.
Everton have now won three successive home Premier League matches for the first time this season.
But it might have been different if Jon Walters had not hit the underside of the bar on three minutes after Robert Huth's header from Ryan Shotton's long throw-in was halted by the agility of Tim Howard in the home goal.
Huth was guilty of squandering an obvious chance on 54 minutes when his free header somehow eluded the home goal from Glenn Whelan's free-kick.
Shotton then saw his header fly past a post from five yards out after Sylvain Distin could not clear a Marc Wilson cross.
Cameron Jerome walloped an effort over from Shotton's backheel on 74 minutes with substitute Charlie Adam seeing Howard repel his free-kick with the last breath of the match.
Everton's best moments came courtesy of the delightful crossing of Leighton Baines in the first period as the England man produced three superb crosses with Nikica Jelavic denied by Huth, Begovic and his own finishing before Mirallas struck what proved to be the winner.
Jelavic had a few chances in the second period, but Everton clung on for dear life.
It was not on the scale of their impressive 2-0 win over Manchester City a fortnight ago, but it may prove to be just as effective in their battle to finish in the top four.
MAN OF THE MATCH
Kevin Mirallas (Everton) - A fine performance from the Belgian player. And an even better goal. Worked hard and was giving a rousing reception before he hobbled off with a leg knock 10 minutes from time.
Everton: Howard 7, Baines 7, Coleman 7, Distin 7, Heitinga 7, Jagielka 7, Gibson 7, Mirallas 8, Osman 7, Anichebe 7, Jelavic 7.subs: Barkley 6
Stoke City: Begovic 7, Cameron 6, Huth 7, Whelan 6, Wilson 6, N' Zonzi 6, Shawcross 7, Walters 5, Crouch 5, Shotton 7, Jerome 6.subs: Jones 6, Adam 6