Jordan Ayew's header on the hour gave Swansea a surprise lead, punishing Newcastle for not capitalising on a host of opportunities to break the deadlock.
However, Swansea's advantage proved all too brief as Joselu, brought on for the profligate Dwight Gayle, levelled matters with a clever finish.
Rafael Benitez's men finished a largely entertaining encounter the stronger of the two sides but could not complete the turnaround.
Newcastle was left to settle for a point that will likely increase the Spanish manager's exasperation at a lack of transfer activity and delays in completing a long-expected takeover.
His side is three points clear of the bottom three while Swansea stays at the foot of the table, four points adrift of safety, and now has the daunting proposition of home fixtures with Liverpool and Arsenal to come.
Newcastle dominated the early exchanges as Swansea struggled to keep hold of the ball, Gayle testing Lukasz Fabianski in the fourth minute with a header that the Pole comfortably saved.
Gayle should have done much better when he headed well wide after good work down the left from Perez, who could find neither power nor direction with an effort from the right of the box after Swansea again surrendered possession.
Paul Dummett lashed over from a Christian Atsu pull-back but the best chance of the half fell to Perez, who burst through on goal after latching on to Matt Ritchie's ball over the top, but was denied by Fabianski as he tried to sneak an effort underneath the goalkeeper's legs.
Former Swansea midfielder Jonjo Shelvey curled well over with a free-kick from the edge of the area, the visitors perhaps feeling justice had been done after Atsu was contentiously deemed to have been fouled.
Swansea will then have felt aggrieved not to have been awarded a penalty as a rare foray forward saw Mohamed Diame appear to block a Mike van der Hoorn effort with his arm.
the visitor was grateful to see the assistant referee Sian Massey correctly raise her flag for offside after Gayle nodded in at the other end.
Gayle wastefully dragged wide four minutes into the second half and Newcastle finally paid the price despite the best efforts of Karl Darlow.
Darlow produced heroics to keep out Ayew's first point-blank header with a fine reaction save but the Ghana forward was there to convert on the rebound.
Swansea's lead lasted just eight minutes, however, as Shelvey unlocked the visitors' defence with a wonderful ball over the top for Perez, whose fortuitously deflected cross fell into the path of Gayle's replacement Joselu to steer back across goal and beyond Fabianski.
Newcastle pressed for a winner without creating many chances to find to it, and Swansea would have stolen the points had Wilfried Bony not seen a goal-bound effort cleared with Darlow stranded, the draw making it just one defeat in four in all competitions for Carvalhal, a run that will provide little solace for the Portuguese given the team's predicament.