The Ryedale side followed up their win at Wheatley Hills the previous weekend in superb style to move eight points clear of the relegation zone.
Malton trailed after two minutes when they were penalised in front of their own posts for offside at a ruck and full-back Stu Waites landed the kick.
The reply was immediate as the Malton pack drove deep into Wests territory and fly-half Charlie Ramsay converted a penalty.
From the restart, Malton pressed again and Ramsay hoisted a kick high and wide, where the aerial challenge was won by winger Leki Atiola. He knocked the ball into the hands of full-back Ian Cooke, and he ran 60 metres to the try-line and Ramsay added the conversion.
Waites kicked another two penalties to reduce the arrears to one point before half-time.
In the opening minute of the second half, Atiola cut through and fed Cooke, who sent flanker Ali Coe powering over in the corner. Ten minutes later, flanker George Harrison took a tap and scrum-half Tom Boyle touched down. Ramsay converted for a 22-9 lead.
Wests narrowed the gap with a catch and drive try from a lineout by number eight Sam Miller.
Waites brought his side to within one score again, but Ramsay gave Malt some breathing space with a 40-metre penalty.
Deep into injury time, West flanker Jon Boatman crossed.
Meanwhile, Pocklington’s stuttering recent form continued with a 9-3 defeat at Morpeth.
Morpeth never looked like scoring a try, but they battled up front, defended with determination and were prepared to sit back and kick goals when the opportunity arose.
For much of the first period Pock camped in the Morpeth half trying to batter the home forwards into submission, but were restricted to a single penalty from Jack Fletcher.
Morpeth made two brief visits to Pock territory and came away with a penalty to make it 3-3 at the break.
It was more even in the second half and Morpeth capitalised on Pock mistakes to kick two more penalties and edge six points clear.
Pock produced a late rally to try to turn the tables, only to be let down by poor execution.
Their lineout had functioned smoothly all afternoon, but when they kicked a penalty to the corner to go for a catch and drive, they gave away the possession.
Teenage centre Josh Britton looked lively when he came off the bench to make his debut, and he raced over, only to be denied for a forward pass.