The form of the Finnish international should have laid the foundation for Villa to pull off a snatch and grab raid.
But Villa striker Dion Dublin saw his 73rd minute penalty saved by Albion goalkeeper Russell Hoult as Villa continue to search for their first away League win of the season.
But they did at least manage to extend their unbeaten run to five games. Albion are now without a win for eight matches, but they should have ended that dismal run against Vila.
Albion dominated proceedings, but were frustrated by an inspired Enckelman. He denied Scott Dobie and Jason Roberts in quick succession after just five minutes and was then relieved to see Â£2.1million Roberts blaze over the bar two minutes later.
Roberts should really have made more of his second chance as he only had Enckelman to beat after outpacing the Villa defenders Mark Delaney and JLloyd Samuel.
With Albion dominating in terms of attacking intent, Villa were rarely seen as a threat and when they did break through Albion goalkeeper Hoult comfortably dealt with two long0range shots from Gareth Barry and Oyvind Leonhardsen.
Enckelman continued to be the far busier of the 'keepers, again denying Roberts and Andy Johnson as Villa managed to battle their way to half-time on level terms.
Referee Dermot Gallagher had no hesitation in pointing to the spot when a surging run by Gareth Barry was ended by a rash challenge from the Albion central defender Darren Moore.
Dublin tried to stroke his spot-kick past Hoult but saw the penalty beaten away by the legs of the former Portsmouth keeper to ensure that honours were even.