Pardew would have been hoping to mark his first game at The Hawthorns with three points against the Eagles, but the Baggies had to make do with a third successive draw in the top flight.
The first chance of the game fell to West Brom's Hal Robson-Kanu, but the forward sent his shot marginally over the crossbar before at the other end, Wilfried Zaha fired into the side-netting after a neat move.
Zaha was a constant threat for Palace and moments after his first effort, the winger sent a deflected shot over the bar, but the game soon descended into a battle in the midfield.
Just before the break, however, Christian Benteke nearly broke his duck for the season in style, with the Belgian getting past three players before seeing his shot saved by Ben Foster, and the striker had a second chance soon afterwards with a header going straight into the hands of the goalkeeper.
As the game moved closer to a conclusion, opportunities began to dry up but Joel Ward - as he had done earlier in the match - had to remain brave to keep a Baggies effort from finding the target.
Salomon Rondon also sent a late effort wide of goal, leaving both clubs having to make do with a point apiece as they extended their respective unbeaten records.
West Bromwich Albion (4-3-3): Foster; Nyom, Evans, Gibbs, Hegazi; Field, Barry (Yacob 30'), Livermore; Robson-Kanu (McClean (72'), Rondon, Rodriguez (Burke 91')
Crystal Palace (4-3-3): Hennessey; Ward, Sakho, Schlupp, Kelly; Milivojevic, McArthur, Loftus-Cheek; Townsend (Sako 87'), Zaha, Benteke