Portsmouth took a 2-1 lead into half-time after goals from Andy Barcham and David Connolly in the 39th and 43rd minutes had cancelled out Ben Hutchinson's 17th minute opener.
But Meikle fired home from close range with 19 minutes remaining to earn a well deserved point for the home side.
Mansfield flew into the lead in the 32nd minute when Ben Hutchinson hit a screaming volley from 25 yards.
But Pompey showed why they are one of the promotion favourites when Barcham levelled after great play by Jed Wallace.
Connolly then turned home a loose ball after Alan Marriott had parried a shot by Barcham to put Pompey ahead.
Mansfield levelled though when sub Lindon Meikle fired home from close-range after Smith had fumbled a hook back from Ollie Palmer.
Meikle, Martin RIley and John Dempster were all denied as Mansfield pressed for the winner in the closing stages.