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A plane flying the banner 'Roberto must go' was followed by a handful of fans in the Gwladys Street End holding up 'Martinez Out' signs and chanting 'Get out of our club' at the end of the 2-1 win over Bournemouth.
Only five home league wins in the last 12 months tells its own story and it is unlikely Baines' goal, after Marc Pugh had cancelled out Tom Cleverley's strike inside the opening 10 minutes, will ease the pressure.
Despite his easy-going appearance, Martinez has a stubborn streak and if his stint at Goodison Park is coming to an end he is determined to go out on his own terms.
The decision to give Oumar Niasse a Premier League debut ahead of 25-goal leading scorer Romelu Lukaku was a bold one which smacked of sticking two fingers up at his critics.
Prior to his full debut Niasse had played just 29 minutes of football since December 10, his last match for Lokomotiv Moscow before a £13.5million January move to Goodison Park.
Just a fortnight ago Martinez had said it would be a "bonus" if he played again for them this season because of his fitness levels but on this evidence he should change that assessment to "unthinkable" as he looked well off the pace.
Martinez's decision to recall goalkeeper Tim Howard, who had not played since January 24 and leaves for Colorado Rapids in the summer, for his penultimate Goodison farewell also did not impress fans.
The American, at least, performed well enough although Pugh's ninth-minute equaliser caught enough of his body before creeping over the line to raise questions among his detractors.
It was no surprise the visitors pegged Everton back, or did it so quickly, as confidence at home has been fragile and even Cleverley's strike two minutes earlier - incredibly from Ross Barkley's first assist of 2016 - failed to settle nerves.
The midfielder's finish was a smart one but so was Pugh's, who swept home Callum Wilson's cross despite Everton complaining the striker had nudged 21-year-old Matthew Pennington, making his Premier League debut, in the back in winning the ball out wide.
Goodison's atmosphere was less toxic than expected - rumoured protests failed to materialise - but still surreal as 20 minutes in Bournemouth fans sang 'Sacked in the morning' to Martinez and pockets of the home crowd applauded.
A minute before half-time Niasse's audacious backheel drifted wide of the far post and, somewhat coincidentally considering his performance, moments later the protest plane flew overhead.
Just when it seemed the day could not get any more odd the 35-year-old Tony Hibbert replaced Muhamed Besic at half-time - 508 days after his last appearance.
Josh King threatened with two efforts but the hosts started to look more threatening.
That was partly because the failed Niasse experiment was ended on the hour with Lukaku sent on to add some firepower.
However, it was winger Aaron Lennon who provided the breakthrough as his run and cross in the 64th minute was rammed home at the far post by Baines, his first goal for 42 matches.
Bournemouth substitute Benik Afobe has two efforts to level things up, the first blocked by Pennington, and such has been their form at home it was something of a surprise Everton did not concede before the end.
TWEET OF THE MATCH
"A plane carrying a banner saying "Time to go Roberto" flies over Goodison." - Everton fans voiced their opinion on manager Roberto Martinez during their match, as Merseyside football writer for The Times Tony Barrett (@TonyBarretTimes) reports.
PLAYER RATINGS
Everton
Tim Howard: 6
Muhamed Besic: 4
John Stones: 5
Matthew Pennington: 7
Leighton Baines: 6
Darron Gibson: 6
James McCarthy: 6
Aaron Lennon: 6
Ross Barkley: 5
Tom Cleverley: 6
Oumar Niasse: 3
Substitutes
Romelu Lukaku (on for Niasse, 60): 5
Kieran Dowell (on for Dowell, 87): 5
Tony Hibbert (on for Besic, 46): 5
Bournemouth
Artur Boruc: 5
Simon Francis: 6
Steve Cook: 6
Tommy Elphick: 6
Charlie Daniels: 6
Matt Ritchie: 6
Andrew Surman: 6
Harry Arter: 7
Marc Pugh: 7
Josh King: 7
Callum Wilson: 6
Substitutes
Junior Stanislas (on for Pugh, 68): 5
Benik Afobe (on for King, 68): 5
Lewis Grabban (on for Wilson, 79): 5
STAR MAN
Matthew Pennington
Handed his Premier League debut the 21-year-old coped admirably with a couple of important blocks and was a touch unlucky for Bournemouth's goal.
MOMENT OF THE MATCH
Aaron Lennon's run and cross for Leighton Baines' winner
It was one of the rare moments of drive and determination.
VIEW FROM THE BENCH
Roberto Martinez made a huge call in starting Oumar Niasse and it backfired spectacularly with the Senegalese looking out of his depth
The team lacked any cohesion or fight and although they won it is unlikely to help their manager
Eddie Howe, meanwhile, is just happy to be in the Premier League next year and his side played like it.
MOAN OF THE MATCH
The protest plane
A feeble effort in all honesty
Whether you agree with them or not at least some fans did it the 'proper' way, remaining behind at the end to hold up banners and chant their discontent.
WHO'S UP NEXT?
Leicester v Everton (Premier League, Saturday May 7)
Bournemouth v West Brom (Premier League, Saturday May 7)
Source : PA
Source: PA