Murphy kicked a penalty and a drop goal in addition to Hillier Rees' first-half try as his side led 11-0 at the interval.
Replacement Evans got Aberavon back into things with three second-half penalties but the Ravens held on.
It was a slow if competitive start to the game as nearly 15 minutes passed before the first scoring opportunity. Aberavon won a kickable penalty inside the Ravens' half but Jamie Davies saw his kick slide wide of the right hand upright.
Bridgend's forwards, who had been in superb form in recent games, had the upper hand, winning one scrum against the head but both sides struggled to create space in open play.
The visitors saw backrower Darryl Thomas hobble off with an injury but with little else of note to report, it remained scoreless with a quarter of the game gone.
After half an hour, Bridgend fly-half Murphy finally got the scoreboard moving with a penalty effort from the right hand touchline to give his side a 3-0 lead.
Aberavon's only glimmer of hope was a break from full-back John Phillips. In plenty of space though, he chose to kick ahead and Murphy covered to avert the danger.
After covering in defence, Murphy turned his attentions to attack and a snap drop goal from the fly-half extended the home side's lead to six.
Further indiscipline from the Wizards saw Murphy given two chances to extend his side's lead but sadly for the home crowd, the fly-half put both difficult penalty efforts wide.
It did not seem to matter though as on the stroke of half-time, the Ravens crossed for the only try of the game. Aberavon turned the ball over and the ball was spread wide to Hillier Rees. Finding himself on the left hand touchline, the No. 8 showed impressive speed to touch down in the corner.
Murphy struck the post with the conversion but his side led 11-0 at the interval.
A half-time deluge did little to liven up the game though it was Aberavon who started the second period the better. Davies put another penalty effort wide and was promptly replaced by Evans at outside-half. The substitute made an instant impact, slotting over a long range penalty to get his side on the board.
Evans soon added a second penalty and after dominating most of the first period, Bridgend led by just five. If the game was now more of a contest, its quality failed to improve with the game mostly played in the middle third.
Substitute Evans kicked a third penalty before Murphy settled the home crowd, slotting over a left-footed drop goal to give his side a 14-9 cushion, one they held onto until the final whistle.