Alan Irvine, appointed as Pepe Mel's successor last month, gave first run-outs to new signings Joleon Lescott, Craig Gardner and Chris Baird against the League Two side.
Irvine made 10 changes at half-time and saw midfielder Dorrans open the scoring in the 54th minute with a right-footed strike from just outside the penalty area.
Striker Berahino doubled Albion's lead with 13 minutes remaining, getting on the end of a throughball before beating a defender and firing home.
Want-away duo Craig Dawson and George Thorne both featured as speculation over their future continues, with Burnley and Derby County respectively keen to sign them.
Albion's victory at their training ground came after they announced the signing of Belgian defender Sebastien Pocognoli on a three-year deal from Bundesliga side Hannover.