Luck was against Forest, with just one win under their belts after promotion last season, the winger's left-foot shot hitting Ian Breckin with keeper Paul Smith wrongfooted on his line.
The Sheffield side, unbeaten at Hillsborough in ten games stretching back to last season, had struggled to make any impact against Forest, looking for their first away points of the season.
Midfielder Chris Cohen tried his luck with a long-range strike before his curling free-kick picked out Joel Lynch, but the defender's low shot was blocked by Richard Wood as Wednesday survived an early scare.
The Sheffield side, struggling to break down a tough Forest defence, should have broken the deadlock when Esajas' precise cross found Deon Burton, but the Jamaica international headed wide from six yards.
Esajas caused more problems for struggling Forest minutes before the break his low curling strike smothered on the line by the diving Smith.
Wednesday snatched the lead three minutes after the re-start. Esajas lost the ball but it rebounded kindly to him and his instinctive low strike took a wicked deflection off centre-back Breckin, before spinning into the net.
Lee Grant pulled off two stunning saves in quick succession, tipping over a fierce Lynch header before producing a carbon copy stop to foil Luke Chambers as Forest looked for a way back.
Wednesday could have had more in the closing minutes. Burton somehow fired wide from a yard out, before Smith foiled Marcus Tudgay with an eye-catching save.
The Forest keeper kept out Burton as Wednesday turned the screw, but he was beaten by the Wednesday striker in the dying minutes, Burton's header clipping the foot of the post.