The opening 20 was dominated by the hosts with a number of attacks going through Josh Hedges, who wriggled his way through on goal on two occasions, but both attempts were blocked.
However, against the run of play, the visitors had the ball in the back of the Salisbury net but it was eventually deemed offside.
Before both sets of fans could catch their breath, the Whites were back up the other end of field swiftly to win a penalty through forward Noah Coppin.
Coppin shaped up for the penalty and slotted the ball with ease into the bottom-left hand corner, giving the Whites the lead going into the break.
Just after the hour mark, Salisbury were able to double their advantage through Odokonyero, scoring his second in the last two games.
Hedges picked up the ball in by the centre circle, dribbled his way through multiple Enfield defenders, squared it to Odokonyero who casually sweeped it into the far corner with his weaker left foot.
The Towners largely struggled to get back into the game after the second as they surrendered to defeat, giving very little threat to the Salisbury net apart from a shot from range with five minutes to spare.
Salisbury move one game closer to survival whilst Enfield face an uphill battle to retain their National League status.