West Ham had a good chance to level up early in the second period but failed to take their rare opening when it arrived, as their wait for a first league point of 2017-18 goes on.
The Hammers struggled to create anything of note in the opening 45 minutes, with home keeper Rob Elliot not having a single save to make.
Newcastle only fared marginally better in front of goal, converting from their first serious attempt as Joselu was given the simple task of netting from close range after Christian Atsu unselfishly squared the ball to him.
Isaac Hayden blasted over the bar and Merino tested Joe Hart with a straightforward save as the Magpies - now with just one defeat in their last 15 meetings against West Ham here - pushed for a second.
They very nearly got it from the final act of the first half, too, as Atsu was given the chance to drive forward before shooting towards the bottom corner, where Hart was well positioned to keep it out.
Newcastle continued to see more of the ball and Ayoze Perez nearly added a second with a decent on-target attempt at the end of a strong charge forward, though the Irons soon managed to find some momentum.
Hernandez, booked for an off-the-ball incident in the first half, was perhaps lucky to still be on the field at that point after a mistimed challenge that went unpunished by referee Neil Swarbrick.
Both teams were beginning to create more in an attacking sense as the match went on, with Hernandez's header needing to be saved by Elliot and Matt Ritchie's curler being pushed to safety by Hart at the other end.
Clark eased the tension around St James' Park 18 minutes from time after glancing home Ritchie's delightful right-sided cross to put the Toon Army well on course for their maiden league win.
There was time for a late Mitrovic goal as, moments after being denied by Hart from a one-on-one position, the substitute striker this time rounded the England international and rolled the ball over the line.