Hamilton-Wickham gave Saturday's run chase an almighty shake, but ultimately fell one short of University at Passmore Oval.
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The hosts relinquished their joint competition lead after finishing 8-376, including four half-centuries, in reply to the Sea Dragons' 6-377 from last weekend.
Hamwicks needed eight runs from the 90th and final over of day two. The scenario was four runs to win and three to tie off the last delivery.
Pumas' batsman Ed Nott (six not out) made two.
University skipper Matt Gawthrop described the round-eight thriller as "the best game I've played in".
Rhys Hanlon (79), Ben Balcomb (76), Tim Studdert (56) and Sam Webber (51) all made fifties. Aqib Zafar (3-126) was the best of Uni's bowlers.
Hamwicks slip to second and Uni, based on other results, also go backwards on the Newcastle District Cricket Association ladder to equal seventh.
Wests now move top of the overall standings, bowling out Charlestown for 165 for a 55-run win at Kahibah Oval.
Rosellas leg-spinner Aaron Bills took 4-30.
And at Learmonth Park, Merewether jumped Charlestown into third after getting the job done against City.
The Lions were six down in reaching City's 186, thanks largely to a 116-run stand between Zac McGuigan (62) and Simon Moore (73).
LADDER: Wests 40; Hamwicks 35; Merewether 34; Charlestown 33, Wallsend 33; Belmont 30; Cardiff, University 29; Stockton 19; Waratah 17; City 15; Toronto 14.
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