The visitors almost took the lead inside the opening 90 seconds, Dayle Rooney's free-kick was sent back into the danger-zone by the head of Cian Byrne and only the crossbar denied Patrick Hickey's audacious back-heel.
At the other end, Clarke found Michael Duffy inside the area, but his effort was straight down the throat of debutant goalkeeper Paul Walters.
Bohs did hit the front in spectacular fashion on 17 minutes, Vaughan playing a one-two with Ross Tierney before unleashing an unstoppable strike into the top-left corner of the net from 25 yards, giving Eddie Beach no chance.
That lead was almost doubled minutes later, as Beach stopped Rooney's low driven effort from just inside the box.
Tiernan Lynch's side were level on 24 minutes, against the run of play as Dos Santos seized on a poor pass from Sadou Diallo, before finding Clarke in acres of space, who showed real composure to score against his former club.
That goal helped the home side grow in confidence and Duffy was denied again by Walters, before Cameron Dummigan blasted wide from inside the area from the resulting corner.