But their failure to do so leaves an opportunity for TATA Steel to snatch the league lead when they take on the same opponents on Wednesday.
Narberth recorded three tries in their win, through winger Matthew Davies, prop Tom Slater and replacement winger Nick Jones. Jon Campbell and Andy Berry crossed for the Students, who remain mired in mid table.
If TATA secure a try-scoring bonus point and win by six points in midweek they will overtake Narberth by virtue of points scored, and they warmed up in style with a 45-11 over Llanharan.
Centre Gbemi Fisher, full back Cameron Clement and outside half Simon Evans all crossed for braces, with number eight Cameron Davies also scoring.
Clement added five conversions to finish with a final tally of 20 points.
Meanwhile Tondu secured a priceless win in the battle to avoid the drop as they earned a 27-20 over visiting Waunarlwydd at Pandy Park.
Tries from Dan Thomas, Matthew Davies and Steve Brown gave the Waterwheelers a 27-6 halftime lead, and, despite a fightback from the visitors, it was enough to climb up two places to tenth.
Ammanford take their place at the foot of the table after succumbing 44-7 to a rampant Bridgend Athletic side at Newbridge Fields.
James Olds, Lyndsey McCausland and Jonathan Phillips crossed for first-half tries, and Phillips converted all three and added three penalties to give the hosts a 30-0 interval lead.
Rhys Ward Jones and Michael Hathaway touched down after the break as Athletic condemned the Recreation Ground outfit to a 10th straight loss.
Bonymaen's situation also looks perilous, but they did at least pick up what could be a crucial bonus point in a 31-28 loss at Llangennech.