With the game in extra time and Yeovil leading 1-0, midfielder Dolan launched his huge effort over goalkeeper Neil Etheridge to help the Glovers through.
Earlier, Saddlers forward Amadou Bakayoko scored an own goal trying to stop Kevin Dawson's header.
Bakayoko hit the crossbar later on as Walsall pressed for a goal.
Match ends, Walsall 0, Yeovil Town 2.
Second Half Extra Time ends, Walsall 0, Yeovil Town 2.
Attempt missed. Kieron Morris (Walsall) left footed shot from outside the box is close, but misses to the left.
Joe Edwards (Walsall) wins a free kick in the attacking half.
Foul by Tahvon Campbell (Yeovil Town).
Attempt missed. Simeon Jackson (Walsall) right footed shot from outside the box misses to the right.
Substitution, Yeovil Town. Omar Sowunmi replaces Tom Eaves.
Tom Eaves (Yeovil Town) is shown the yellow card for a bad foul.
Rico Henry (Walsall) wins a free kick in the defensive half.
Foul by Tom Eaves (Yeovil Town).
Attempt saved. Tahvon Campbell (Yeovil Town) right footed shot from outside the box is saved in the centre of the goal.
Attempt missed. Kieron Morris (Walsall) left footed shot from outside the box misses to the left.
Matthew Dolan (Yeovil Town) is shown the yellow card for excessive celebration.
Goal!  Walsall 0, Yeovil Town 2. Matthew Dolan (Yeovil Town) left footed shot from more than 35 yards to the top left corner.
Joe Edwards (Walsall) wins a free kick in the defensive half.
Foul by Tahvon Campbell (Yeovil Town).
Jason McCarthy (Walsall) wins a free kick on the right wing.
Foul by Tom Eaves (Yeovil Town).
Joe Edwards (Walsall) is shown the yellow card for a bad foul.
Foul by Joe Edwards (Walsall).
Tahvon Campbell (Yeovil Town) wins a free kick in the defensive half.
Second Half Extra Time begins Walsall 0, Yeovil Town 1.
First Half Extra Time ends, Walsall 0, Yeovil Town 1.
Amadou Bakayoko (Walsall) hits the bar with a left footed shot from the centre of the box.
Goal!  Walsall 0, Yeovil Town 1. Tahvon Campbell (Yeovil Town) header from the centre of the box to the top left corner. Assisted by Ryan Hedges with a cross following a set piece situation.
Joe Lea (Yeovil Town) wins a free kick in the defensive half.
Foul by Matt Preston (Walsall).
Substitution, Yeovil Town. Tahvon Campbell replaces Otis Khan.
Attempt blocked. Amadou Bakayoko (Walsall) left footed shot from outside the box is blocked.
Joe Edwards (Walsall) wins a free kick on the left wing.
Foul by Tom Eaves (Yeovil Town).
Attempt missed. Rico Henry (Walsall) left footed shot from outside the box is too high.
Foul by Liam Kinsella (Walsall).
Ryan Hedges (Yeovil Town) wins a free kick in the defensive half.
Attempt blocked. Otis Khan (Yeovil Town) right footed shot from the centre of the box is blocked.
Foul by Liam Kinsella (Walsall).
Kevin Dawson (Yeovil Town) wins a free kick in the attacking half.
First Half Extra Time begins Walsall 0, Yeovil Town 0.
Second Half ends, Walsall 0, Yeovil Town 0.
Corner,  Yeovil Town. Conceded by Neil Etheridge.
Yeovil Town's Matthew Dolan scored a goal from inside his own half as the League Two side reached the EFL Cup second round with a win a Walsall.