The Ivorian stabbed home from close range in the eighth minute after a series of errors.
Filipe Morais had a shot from 12 yards well saved by Trevor Carson and Lucas Akins had a rebound blocked before Zoko poked into the middle of the net with his right foot.
The 30-year-old doubled his tally in the 38th minute, this time with his left.
Yassin Moutaouakil allowed the Boro frontman to dribble around him on the edge of the area before Carson failed to block a pacey shot destined for the middle of the net.
Pompey's Gavin Mahon was sent off for elbowing Morais while contesting a header five minutes into the second-half but David Connolly's 71st minute tap-in gave the vocal visiting fans hope.
The 36-year-old was gifted the opportunity by Ryan Bird, who passed the ball around an on-rushing Chris Day.
Joe Devera was picked out at the back post by an injury time corner but fired wide and moments later Danny East headed over from another set piece.
Morais almost sealed the win but fired an 83rd minute effort from 20 yards wide.