(Newcastle win 3-2 on aggregate)
Newcastle's veteran duo Alan Shearer and Gary Speed were on target to clinch a place in the Uefa Cup semi-final.
Shearer headed Newcastle in front after nine minutes when he powered home a near post corner from Laurent Robert.
PSV were level five minutes after half-time when Mateja Kezman equalised from the penalty spot following Olivier Bernard's foul on Ji-Sung Park.
But Speed confirmed a last four clash with Marseille by heading home another Robert corner after 66 minutes.
It put Newcastle in the semi-final of a European competition for the first time in 35 years, when they won the Inter Cities Fairs Cup.
Newcastle boss Sir Bobby Robson insisted the first goal would be crucial - and Shearer typically obliged after only nine minutes.
John de Jong needed a desperate block to deny the Newcastle captain, but when Robert swung in a near post corner, Shearer made no mistake with a flashing header.
And Titus Bramble should have doubled Newcastle's advantage four minutes later when he missed the ball completely after Darren Ambrose's cross found him unmarked only three yards out.
9 mins: Alan Shearer heads Newcastle in front
50 mins: Mateja Kezman equalises from the penalty spot
66 mins: Gary Speed heads Newcastle back in front
Robert's corners were proving a potent weapon, and a far post delivery was diverted over the top from point-blank range by Jermaine Jenas.
PSV made an interval change, bringing on Jan Vennegoor of Hesselink for Dennis Rommedahl.
And it reaped rewards as the Dutch side drew level after 50 minutes from the penalty spot.
Bernard was the culprit with a clumsy challenge on Ji-Sung Park and Kezman punished Newcastle by beating Shay Given from the spot in comprehensive fashion.
Bramble wasted another glorious chance to restore Newcastle's lead after 61 minutes, heading over the top from Robert's dangerous free-kick.
Speed was more successful when another fiercely struck Robert dead ball, this time from a corner, found him unmarked to head powerfully home from inside the six-yard box.
PSV pressed forward as time ran out, and Given needed to be at his best to save a 25-yard free-kick from Wilfred Bouma.
Newcastle: Given, Hughes, Woodgate, Bramble (O'Brien 78), Bernard, Ambrose (Ameobi 81), Jenas, Speed, Robert (Viana 90), Shearer, Bellamy. Subs Not Used: Harper, Elliott, Dyer, Bridges.
PSV: Waterreus, Bogelund, Colin, Bouma, Lee, De Jong, Vogel (Vonlanthen 75), Van Bommel, Park, Kezman, Rommedahl (Vennegoor of Hesselink 45).
Subs Not Used: Van Dijk, Addo, Wuytens, Van der Schaaf, Do Bonfim.
Referee: Manuel Enrique Mejuto Gonzalez (Spain).