St Johnstone goalkeeper Enckelman saved brilliantly from Nick Blackman and Rob Milsom, before Langfield emulated his efforts under sustained second-half pressure from the home side, who were inspired by the recalled Peter MacDonald.
The stalemate leaves the teams locked together in the SPL, three points off the top six and level with Hibernian on 31 points.
A draw was not much use to either in their quest to make the top half of the table, but Saints came closer to finding a win after a quiet first half.
The clean sheet was their seventh in a row at McDiarmid Park and came despite the introduction of Blackman for Aberdeen, who replaced the suspended Chris Maguire after scoring four goals for Motherwell against the Perth side earlier in the season.
The St Johnstone defence included Graham Gartland after Michael Duberry suffered a groin injury early in Sunday's 4-0 defeat by Rangers, and the home side's strikeforce impressed in the early stages.
Collin Samuel and MacDonald looked lively up front and the latter came close with a header and volley, both from tight angles.
Aberdeen had a great chance midway through the first half when Blackman was threaded through by Scott Vernon, but Enckelman narrowed the angle and blocked the striker's low shot from 15 yards with his feet.
MacDonald soon threatened again when his persistence got him in behind the Dons defence, but Langfield quickly blocked from the striker.
Both sides struggled for creativity on the bumpy pitch as the half progressed.
Enckelman produced a stunning save in the opening stages of the second half, tipping over Milsom's powerful strike from 16 yards after Sone Aluko's impressive run and cutback.
David McNamee came across to clear as Samuel appeared set to finish MacDonald's square ball, and Langfield then came to Aberdeen's rescue by getting down to stop Dave Mackay sliding the ball into the corner after a one-two with MacDonald.
MacDonald created another chance when he cut the ball back for Danny Invincibile, but Langfield produced another superb one-handed save to stop the cushioned volley, and Samuel headed over from close range after his strike partner had returned the ball.
Yet again MacDonald set up a team-mate when he headed into the path of Liam Craig but Langfield made another save, coming off his line to block the midfielder's low shot, and substitute Nikola Vujadinovic bravely cleared as Murray Davidson slid in for the rebound.
St Johnstone kept up the pressure and they were denied a strong penalty claim by Craig Thomson in the 82nd minute following McNamee's clumsy aerial challenge on MacDonald.
Substitute Stevie May missed their last chance in the final minute when he shot wide following Mackay's cutback.