Winnall struck in the 77th minute, breaking free into the box to steer his shot past keeper Scott Flinders.
It came after Hartlepool had looked likely to extend their five-match winning run.
And in the second half Andy Monkhouse rattled the post with a deflected shot.
"Hartlepool were a team full of confidence and it was a tough game for us," said Scunthorpe boss Laws.
"We did not play as well as we know we can. We will play better than this and lose.
"We weren't passing the ball well, which is key to the way we play.
"We had to find a way to win the game and we switched our formation to play an extra man in the middle of the park.
"In the end it was one good direct ball that opened things up for us and young Sam took his goal really well.
"Sam always gets chances and he is in good form for us at the moment. He wants to finish top scorer in this division.
"We are not scoring a lot of goals at the moment and we are relying on Sam a lot."
Laws was also pleased with his side's defensive resilience after a seventh clean sheet in 13 games this season.
"We know we can play better than this, but credit to the players, they dug deep to get us the result we wanted," added the Iron manager.
"We needed Sam Slocombe to help us out in the first half with a couple of good saves - but that is what he is there for.
"After losing 4-0 at home to Exeter a week ago, we have responded well with two clean sheets, first at Fleetwood and then again here again today."
- Sports & Recreation
- Sam Slocombe
- Scott Flinders