The Eagles relied heavily on their forwards and hooker Gustav du Rand found the tryline off the back of the maul early on.
Scrumhalf Branden de Kock slotted a penalty for UDubs, before NWU scored their second try through lock Jeandré Leonard.
Flyhalf Keagan Fortune missed both conversions but slotted a penalty to make it 13-3 at half-time.
The start of the second half was dominated by NWU's forwards, with No 8 André Fouché going over for their third try.
Left wing Lungi Msenge’s converted point-of-origin try put UDubs back within striking distance of the Eagles at 20-15.
But NWU No 11 Charl Pretorius took the game away from them when he scored his team’s bonus-point try.
Fortune then kicked a penalty after UWC winger André Manuel had been sent to the sin bin for the remainder of the game.
FNB Player That Rocks: Jeandré Leonard (FNB NWU Eagles)
FNB NWU Eagles – Tries: Gustav du Rand, Jeandré Leonard, André Fouché, Charl Pretorius. Conversion: Keagan Fortune. Penalties: Fortune (2).
FNB UWC – Try: Lundi Msenge (1x7). Conversion: Branden de Kock. Penalties: De Kock (2).
Report courtesy varsitycup.co.za. Photo by Christiaan Kotze/FNB Varsity Cup