Collegiate fullback Todd Inness and winger Ruslan Casey had a tough time keeping the pill under control, while first-five Stephen Perofeta ran some promising plays he was offline with some of his clearances in the wind.
As always in a mudlark, it fell to the loose forwards to try to salvage opportunities and although they were getting a pounding on attack and defence, No8 Joe Edwards and captain flanker Albert Te Atuarere never quit trying.
Wellington got back on attack after halftime with centre Pepesana Patafilo cutting through the last defender to score after buildup from Collegiate fumbling the bomb kick.
Halfback Kemara Hauiti-Parapara then darted blindside from a 15m scrum and drew the last line to give reserve winger Franscois Swartz enough room to dive over.
Collegiate wouldn't lie down as Edwards strove forward from a series of tap kicks, which second-five Charlie McCartin followed up as he came close to slipping through the line.
Breaching Wellington's 10m zone, Collegiate got the momentum to give McCartin another crack and he forced his way over for 24-10.
That scoreline might have been a fairer reflection of the contest, but Wellington were not done as Fuli went on a barging run before his team spread to reserve back Donell Anae to slide over inside the final minute.
Wellington College 31 (C Fuli, S Robinson, P Patafilo, F Swartz, D Anae tries, Swartz 2 con, K Hauiti-Parapara con) beat Wanganui Collegiate 10 (C McCartin try, S Perofeta pen, con). HT: 12-3.