The game did come to life late on with Ats Purje wasting a good chance for Estonia before Breel Embolo's trickery forced Ragnar Klavan to bundle the ball into his own net in stoppage time.
Xherdan Shaqiri had been Switzerland's most likely goalscorer in the first half before he was substituted.
The second half was littered with substitutions and stoppages before the late excitement.
Switzerland ended with 21 points, nine behind group winners England who won all 10 of their games.
Estonia ended with 10 points, six behind Slovenia who will enter the playoffs.
(Reporting by Martyn Herman, editing by Ed Osmond)
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