The home side took the lead through Denis Epstein, who got behind the Newcastle defence and slotted past Stephen Harper.
But Newcastle, playing their first European match for six years, dominated thereafter and made their superiority pay when Taylor fired in a superb free-kick from 25 yards.
Chances fell to Gabriel Obertan, Demba Cisse and Romain Amalfitano in the second half - but Atromitos held firm to take a draw with an away goal to the SportsDirect Arena.
With temperatures having touched 37 degrees during the day in Athens, the pace of the game was always going to be slow as Newcastle returned to European competition for the first time since they were dumped out of the UEFA Cup by AZ Alkmaar on away goals in 2006-07.
Despite the heat – and the long list of first-team regulars absent - Newcastle seemed to be coasting early on.
But young James Tavernier struggled to get to grips with German wide man Epstein, who exposed the full-back’s poor positioning with several good runs into the box.
So it was somewhat inevitable when Epstein evaded Tavernier’s attention to latch onto Nikola Beljic’s through ball, and slot confidently beyond Harper.
Rather than build on their advantage, Atromitos sat back and invited more Newcastle pressure.
And the Magpies got their reward for their first-half superiority after Dan Gosling was fouled by Matias Iglesias. Taylor, as he has so often done before, swept the 25-yard free-kick over the wall and beyond Atromitos keeper Charles Itandje with the last kick of the half.
Newcastle looked the more likely to grab the winner in the second half, with Obertan coming closest when he flashed a shot just over from 20 yards after Cisse had cushioned the ball back to him.
Cisse could have scored the winner himself when Itandje hopelessly missed Obertan’s cross from the right – but recovered to smother Cisse’s effort.
Substitute Amalfitano could have netted the winner late on when Cisse back-heeled the ball into his path, but Amalfitano’s first ouch let him down and Itandje gathered.
On a low-key night when Alan Pardew rested the likes of Fabricio Coloccini, Cheick Tiote and Demba Ba the draw represented a solid start in Europe for the Magpies, ahead of next Thursday's return leg.