Newcastle United's bleak midwinter continues. Alan Pardew's injury-hit side have now lost nine of their last 11 Premier League games and, despite there being much to applaud about their contribution to an exhilarating match, life after Demba Ba may not be easy.

Everton headed back across the Pennines still harbouring very real hopes of Champions League qualification but David Moyes's side will know they might have struggled to collect all three points had it not been for another superlative performance from Leighton Baines. The left-back scored the equaliser and his crossing and dead-balls kicking tormented Newcastle throughout to the extent that he might easily have completed a hat-trick.

"To come to St James' Park you have to play very well because you are going to come up against one of the top teams in the Premier League," said Moyes. "I think Newcastle are in a false position. They're a strong team with a strong manager."

Pardew needs such staunch support right now. "Let's be honest, we're on an awful run," he said. "Everton had a little bit more guile, a little more quality, a little more experience. I need to get some players out of the treatment room and my best side out on the pitch because I can't hide that we're right in trouble."

Even so Moyes's players were insufficiently wary when, in the second minute, their defence misread Tim Krul's long punt forward. With both Johnny Heitinga and Sylvain Distin missing the ball, it fell to Papiss Cissé, running beyond them, to direct a looping header over Tim Howard and into the net."Are you watching Demba Ba?" chorused the Gallowgate end. The Senegal striker had fled the city earlier in the day, high-tailing it to Heathrow for talks with Chelsea after the west London club triggered the £7m release clause in his contract. "Demba goes with our blessing," said Pardew.

After seeing his side concede 11 goals in their previous two games – admittedly against Manchester United and Arsenal – the manager knew Mike Ashley, Newcastle's owner, would expect an improvement. Aiming to deliver it, Pardew replaced Ba with Shola Ameobi – who it seems will not now be playing for Nigeria in the Africa Cup of Nations after all – in a fluid 4–2–3–1 formation with Cissé stationed wide on the right.

If the Senegalese's opener offered Pardew hope, however, Moyes's side could have swiftly equalised when a typically swerving Baines free-kick seemed goal-bound until Krul somehow diverted it for a corner.

The Merseyside club were starting to find their range, although they were betrayed by Marouane Fellaini's heavy touch which enabled Davide Santon to make a vital interception as the Belgian shaped to shoot. At the other end James Perch's header rebounded off a post and Mathieu Debuchy, the watching France right-back – expected to finalise his £5.5m move from Lille on Thursday – must surely have been impressed by his new team-mates' endeavours.

Debuchy, may, however be relieved to learn that Newcastle have now played Everton twice in the league, thereby dictating that, any FA Cup pairing excepted, he will not have to keep an eye on Baines this season. "I wish I'd had Debuchy here in time to mark Baines," Pardew added. "We could have done with him."

Everton can never be underestimated from set pieces – and especially not when a left-back Moyes believes is now England's best is taking them. So it proved shortly before half-time when Baines's equalising free-kick, awarded for a rather soft foul on Fellaini, left Pardew shaking his head.

Delivered at vicious velocity from at least 35 yards it dipped and curved, thoroughly deceiving Krul. The Dutch goalkeeper had earlier saved superbly from Pienaar after the South African met Baines's beautifully weighted through-pass but he could not adjust his position in time to make a stop this time.

Newcastle, who thought they might have had a penalty when Ameobi crumpled under Phil Neville's challenge, tried to raise the tempo once more but Moyes's decision to replace Steven Naismith with Victor Anichebe was to prove hugely inspired. Almost immediately after coming on, the forward was well placed to step inside Santon and shoot beyond Krul after Nikica Jelavic had drifted past Fabricio Coloccini and delivered a low centre in his direction.

Subsequent chances followed at either end but Baines had already done more than enough to ensure it was Everton's night.