The Tangerines took an early lead from a Matt Dickenson drag flick penalty corner into the top corner in the second minute before doubling their advantage with a Sam Lynn finish from an acute angle.
The first half remained an even encounter with the Acomb midfield controlling the game through man of the match Paul Wright, Dave Richardson, Dickenson and Mark Gibbons.
Thirsk pulled a goal back ten minutes into the second half via a deflection past ’keeper Craig Brown.
But, five minutes later, Dave Brown clinically punished the opposition by striking sweetly into the net.
Thirsk were gifted a second goal by a calamitous rush by Brown, who missed the ball to enable a Thirsk raider to walk the ball into an empty goal.
But Acomb secured the points with seven minutes remaining with a penalty stroke scored by Dickenson.
Acomb are now second ahead of taking on the unbeaten leaders Bradford University I.