In-form keeper John Higgs ensured a point for Lynn, who remain in sixth as results elsewhere went their way.
Higgs denied ex-Birmingham midfielder Howard Forinton with eight minutes remaining as The Walks outfit weathered a late second half storm.
A draw was a good result at The Grove, which has been an unhappy hunting ground for the Linnets in recent years.
Saturday’s stalemate means Lynn have gone four hours without scoring at the Yeltz’s headquarters, but gained their first point there in four games.
On a sticky pitch both sides huffed and puffed, but Lynn defended stoutly to keep their third clean sheet in four games.
That they have done so is partly the work of Higgs, who has hardly put a foot wrong this season since securing the number one goalkeeper’s jersey.
After impressing in the midweek cup win, manager Tommy Taylor retained Dean West and Mark Camm in the centre of defence, using Grant Cooper as a holding midfielder and keeping youngsters Stephen Harvey and Luke Fell in the side.
Taylor said: "Blooms had the best two chances. We had the ball in good areas but gave it away.
"We’ve got to create a bit more. I changed the system and I put Adam Smith in a more forward role.
"Jonesy in the second half was excellent. Give me another 20 clean sheets and I’ll be happy.
"Higgsy had to make two saves and did very well. Danny Hammond was unlucky not to score. The ball was going in but hit the back of someone’s heel."
Adam Jones started as Sam McMahon was unavailable due to his son being taken to hospital on Friday night.
Among the few first half chances were Fell shooting straight at keeper Dean Coleman and Cooper’s 25 yard effort being deflected by Dave Haywood over the bar.
The league’s leading scorer Danny Bloomfield fired wide when set up by Smith.
At the other end, Halesowen captain Steve Pope struck over from a corner while Higgs saved at the feet of Yeltz top scorer Nathan Lamey, and thwarted both Forinton and dangerman Alex Cowley.
Early in the second half Bloomfield turned and volleyed outside the box but was inches wide.
Lynn made a couple of changes before the game heated up. Jones cleared off the line from Cowley, while Ian Cooper nodded wide of the Lynn target at a corner.
Lynn sub Hammond, who replaced Cedric Anselin (who Taylor felt was ineffective on the day) had an effort blocked on 80 minutes.
Lamey sent Forinton clear late on - but Higgs was up to the task, diving low to his left to bring off that crucial stop.
Halesowen: Colman, Cooper, Haywood, Preston, Pope, Knight, Cowley, Lamey, Forinton, Forsdick (C. Smith 86), Amos (N. Smith 77). Subs not used: Pierpoint, Johnson, Strachan. Booking: Lamey.
Lynn: Higgs, West, Smith, Harvey, Cooper, Jones, Fell (Defty 70), Anselin (Hammond 66), Camm, Bloomfield, O’Halloran. Sub not used: McNeil.
Referee: S. Pardoe (Crewe).
MoM: John Higgs.