Experienced goalkeeper Ali Al Habsi was making his debut for the visitors after joining on loan from Wigan Athletic, and he made a strong save at his near post after Matt Richie had exchanged passes with Andrew Surman to set up a shooting chance.
Artur Boruc at the other end was completely untested in the early stages as Joao Teixeira passed up several shooting opportunities, with a deflected Gary Gardner free kick the closest that Brighton came before the opening goal.
Scotland international defender Greer headed a Simon Francis cross into his own net on 25 minutes to encapsulate the bad fortune that Sami Hyypia's side have endured during their 10-match winless run in the league.
Albion were level within four minutes, though, as Liverpool loanee Teixeira slipped an inch-perfect pass through for Colunga to round Boruc and slot into the empty net for his first Brighton goal.
Bournemouth, who have won their last five matches in all competitions, regained the lead seven minutes prior to the break when a cross was allowed to travel to Pugh at the back post, and the midfielder smartly volleyed the bouncing ball into the bottom corner via a slight deflection.