© Getty Images
Hosts Hibs controlled large parts of the opening 45 minutes, but they were unable to call Lee Hollis in the Motherwell goal into any telling action.
Their best chance came in the 58th minute, but debutant James Collins failed to guide his header from close range on target.
It appeared that both goalkeepers were going to keep clean sheets until Anier intervened in the closing stages.
The Estonian collected a pass that had floated over the top of the home defence, before firing into the bottom corner of the net.
Hibs had more of the possession thereafter, but the visiting rearguard held firm to collect all three points.