Wotton struck from a controversial second minute penalty and then a hammer of a free-kick in stoppage time.
Alex substitute Luke Rodgers' effort midway through the second half set up a tense finish for Tony Pulis' men but Crewe offered little to suggest they might snatch a draw.
The Railwaymen had new signings Gareth Taylor and Jon Otsemobor making their debuts and the former offered an outlet with his ability in the air.
But he blazed a chance wide after 35 seconds and it proved costly when David Vaughan slid in on David Norris and referee Darren Drydale pointed to the spot.
Wotton made no mistake by firing a rising drive beyond Ross Turnbull into the top left-hand corner.
Crewe came close to an equaliser in the 17th minute when Steve Jones got on the end of Turnbull's long kick and brought a reaction save out of Romain Larrieu with a snap-shot on the turn.
And Vaughan really should have tucked Jones' cross away but failed to connect cleanly with his head and sent the ball wide from eight yards out.
Norris was outstanding down the right flank for the visitors, but he guided a great chance from a Mickey Evans flick-on wide of the far post with the goal at his mercy.
But he needn't have worried as Richard Walker's foul on Evans allowed dead ball specialist Wotton to size up goal from 25 yards out and he hit a powerful drive through the wall and Turnbull's hands for the second.
At 2-0 down it looked a hopeless task for Crewe but Jones could have reduced the arrears five minutes after the break when he took the ball through on the right of the box, but instead of shooting attempted to round Larrieu only for the keeper to get his hand on the ball.
Turnbull redeemed himself when he blocked off Nick Chadwick's near post effort.
And Rodgers threw Crewe a lifeline in the 68th minute after Plymouth made a hash of a long Kenny Lunt free kick. Jones headed back across the box and Rodgers took the dropping ball with a neat half-volleyed finish into the bottom corner.