But they remain second in their Europa League group and qualification remains in their own hands with two games left to play.
Everton started at a high tempo, with Diniyar Bilyaletdinov industrious on the left and Jack Rodwell impressing from his deep midfield position.
But there was a lack of composure to their play at times and the home team were guilty of wasting promising positions by looking for a killer pass too early.
They did create a few openings and Marouane Fellaini forced an early save from Cesar with a long-range strike, Leighton Baines had a shot blocked, Yakubu shot wide from a tight angle and Tim Cahill headed straight at the Benfica keeper.
But it was the away team who came closest to breaking the deadlock just before the break after an opening half of few clear openings.
A precise Fabio Coentrao cross from the left was met by Cardozo but his header hit the base of the post and rebounded towards Saviola.
The Argentine shot crisply at goal with his right foot and it took a superb reaction save from Howard to ensure the home team reached the break on level terms.
Benfica scored three goals in quick succession at the start of the second half in Portugal and almost took the lead after 57 minutes at Goodison Park.
Cardozo pierced the Everton defence with a brilliant curved through ball that sent Di Maria through on goal but he shot over from 20 yards.
Di Maria almost atoned for his miss with an audacious long-range shot from a wide position that the alert Howard tipped over his crossbar.
Benfica had started to find their range with some precise attacking football and unsurprisingly took the lead through Saviola.
The visiting team broke with a sweeping move that culminated with Saviola fortuitously gathering a ricochet off Di Maria before slotting the ball beyond Howard.
Benfica looked even more assured in possession after taking the lead, while Everton adopted an increasingly deep defensive line as they tried to nullify their opponents' attacking threat.
The match was put beyond Everton when another scintillating attack culminated with Ruben Amorim's shot deflecting into the path of Cardozo for the Paraguayan to slot the ball across Howard and into the bottom corner.
Howard appealed for offside and he had a strong case as replays suggested Cardozo was beyond the last Everton defender as Amorim shot.
Distin should have ensured a dramatic finish after a partially blocked shot fell invitingly to him but he failed to convert from six yards.
Everton manager David Moyes: "We have tough games coming up and we knew the group was never going to be easy and it will prove that way, I am sure.
"I think Benfica are a good side and it was a tough game but it was tighter than the last one (where Benfica won 5-0).
"We became a little open in the second half, maybe trying to score, and we got done on the counter for the first goal. We still had four defenders back though, and the goals weren't like the goals in Benfica.
"One ricocheted off our player and fell to them, so I didn't think the goals were beautiful; they were poor defensive moments for us."
44:38 Inswinging corner taken by Alexandre Fabio Coentrao from the right by-line played to the near post, Tim Cahill manages to
make a clearance.
44:07 Sylvain Distin concedes a free kick for a foul on Oscar Cardozo. Alexandre Fabio Coentrao crosses the ball from the free kick
left-footed from right wing, Marouane Fellaini manages to make a clearance.
40:59 Tony Hibbert challenges Angel Di Maria unfairly and gives away a free kick. Angel Di Maria takes the free kick.
40:28 Javier Saviola takes a shot. Save by Tim Howard.
40:00 Centre by Alexandre Fabio Coentrao, Headed effort from inside the area by Nascimento Ramires hits the post.
39:11 Angel Di Maria takes the outswinging corner, clearance by Tim Cahill.
37:46 Foul by Javier Saviola on Joseph Yobo, free kick awarded. Free kick taken by Joseph Yobo.
35:53 The referee blows for offside. Jacobi Julio Cesar takes the free kick.
34:53 Jack Rodwell has an effort at goal from just outside the box which goes wide of the right-hand post.
34:39 Dan Gosling crosses the ball, clearance made by Anderson Luisao.
31:58 A cross is delivered by Diniyar Bilyaletdinov, Tim Cahill takes a shot. Comfortable save by Jacobi Julio Cesar.
31:25 Angel Di Maria crosses the ball, clearance by Sylvain Distin.
29:36 Ayegbeni Yakubu produces a right-footed shot from outside the penalty box and misses right.
27:47 Short corner worked by Ayegbeni Yakubu.
27:32 Centre by Ayegbeni Yakubu, save by Jacobi Julio Cesar.
27:20 Centre by Tony Hibbert, Filipe Ruben Amorim manages to make a clearance.
26:32 Alexandre Fabio Coentrao gives away a free kick for an unfair challenge on Ayegbeni Yakubu. Leighton Baines takes the direct
25:55 The ball is crossed by Marouane Fellaini.
25:22 Ayegbeni Yakubu is caught offside. Rechel Sidnei takes the free kick.
24:49 Foul by Dan Gosling on Angel Di Maria, free kick awarded. Free kick taken by Marinho David Luiz.
24:02 The ball is swung over by Leighton Baines, Francisco Javi Garcia makes a clearance.
21:30 Diniyar Bilyaletdinov produces a cross, Nascimento Ramires makes a clearance. Leighton Baines takes a shot. Anderson Luisao
gets a block in. Long range effort by Jack Rodwell goes wide right of the net. Marouane Fellaini is penalised for a handball.
Direct free kick taken by Rechel Sidnei.
21:05 Unfair challenge on Jack Rodwell by Oscar Cardozo results in a free kick. Direct free kick taken by Sylvain Distin.
19:30 Booking Booking for Ayegbeni Yakubu for unsporting behaviour.
18:41 Unfair challenge on Nascimento Ramires by Ayegbeni Yakubu results in a free kick. Free kick taken by Anderson Luisao.
17:46 Unfair challenge on Ayegbeni Yakubu by Anderson Luisao results in a free kick. Leighton Baines takes the direct free kick.
16:57 Corner taken right-footed by Nascimento Ramires, Leighton Baines manages to make a clearance.
16:49 The ball is swung over by Alexandre Fabio Coentrao, blocked by Tony Hibbert.
14:33 Shot from inside the area by Ayegbeni Yakubu clears the bar.
13:59 Unfair challenge on Dan Gosling by Marinho David Luiz results in a free kick. Joseph Yobo takes the direct free kick.
13:03 Angel Di Maria takes a shot. Save made by Tim Howard.
12:37 Alexandre Fabio Coentrao fouled by Dan Gosling, the ref awards a free kick. Marinho David Luiz restarts play with the free
10:46 The ball is sent over by Ayegbeni Yakubu.
7:59 The referee blows for offside. Direct free kick taken by Jacobi Julio Cesar.
7:32 Filipe Ruben Amorim concedes a free kick for a foul on Marouane Fellaini. Leighton Baines restarts play with the free kick.
6:05 The ball is crossed by Dan Gosling, Nascimento Ramires manages to make a clearance.
3:31 Centre by Angel Di Maria, Tim Howard makes a save.
3:05 Marouane Fellaini takes a shot. Jacobi Julio Cesar makes a save.
1:58 Free kick awarded for a foul by Joseph Yobo on Oscar Cardozo. Rechel Sidnei restarts play with the free kick.
0:00 The referee gets the match started.
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