Hungarian international midfielder Gera's fifth goal of the season in the 63rd minute continued Albion's recent revival as they secured their third win in four games to move level on points with fourth bottom Southampton.
Albion looked doomed to relegation at Christmas when they were rooted to the bottom of the table. But they are unbeaten at the Hawthorns since Boxing Day and a run of ten points from the last five games has given them genuine hope that they can avoid an immediate return to the Championship.
While Albion's season is on an upward curve, David Moyes' side is making hard work of trying to secure a money spinning place in the Champions League.
They have now collected just four points from the last 18 and, apart from a late rally, struggled to ever look like ending their recent poor run.
Albion, who were boosted the day before game when their main relegation rivals, Southampton, Crystal Palace and Norwich City, all lost, were the width of the crossbar away from taking the lead after just ten minutes.
They won a free-kick on the right-wing after Everton full-back Alessandro Pistone hacked down Geoff Horsfield.
Jonathan Greening whipped in a cross and Thomas Gaardsoe rose above the Everton defence only to see his header beat goalkeeper Nigel Martyn but crash off the bar.
In a game that was punctuated by a succession off free-kicks, clear-cut chances were hard to come by.
Everton, who started with Marcus Bent as a lone striker, struggled to break down Albion's rearguard. On the one occasion in the first-half when they did create an opening after a neat throughball from Tony Hibbert, Bent fluffed the chance by shooting weakly at goalkeeper Russell Hoult.
With the stakes so high for both sides there was a distinctly competitive edge to proceedings.
Everton's Australian international midfielder Tim Cahill showed that when he became the first player to be booked by referee Graham Poll for a rash challenge on Martin Albrechtsen in the 27th minute.
The game threatened to boil over at this stage - especially when Albion midfielder Kieran Richardson followed him into the book 60 seconds later for an ill-timed challenge on Mikel Arteta.
But Poll managed to keep a lid on proceedings as Albion took something of a stranglehold on proceedings in the closing stages of the first-half, during which Cahill needed to be well placed to clear a goalbound header from Neil Clement.
While Albion may have held the upper hand in the first period, Everton proved to be more of a threat after a half-time pep talk from Moyes.
Bent suddenly started to cause panic among Albion central defenders Gaardsoe and Neil Clement with the impressive Leon Osman and Cahill providing support from midfield.
But the finished product continued to prove elusive with Bent firing high over the bar in the 61st minute from the edge of the area after being set-up by good work from Arteta.
It proved to be a costly miss by Bent as Albion broke the deadlock just two minutes later.
Albion left-back Paul Robinson collected a mis-placed free-kick from team-mate Ronnie Wallwork on the left wing and fed a short pass to Greening.
The former Manchester United midfielder whipped in a perfect cross that picked out Gera, who beat Martyn at the far post with a well placed header.
Albion should have increased their advantage eight minutes after Gera struck, only for the woodwork to again deny them when Albrechtsen rattled the post with a low drive.
Moyes sent on old war horse Duncan Ferguson for the final 20 minutes to try and give Everton more of a threat in attack.
The move almost paid off as it gave Bent more freedom but the former Ipswich Town marksman continued to squander the chances that came his way.
Hoult beat away his fierce 80th-minute drive before Bent dragged his shot across the face of goal when again well placed a minute later.
Gera was then denied a second goal two minutes from time after Martyn did well to block his low drive from a Geoff Horsfield cross.