Nathalie Bjorn’s second-half penalty was enough to seal all three points for her team, a win that lifts them to eighth place in the table.
The Toffees had gone in front on 54 minutes when Anna Patten deflected Sara Holmgaard’s rasping centre into her own net.
The Villans responded immediately through England forward Rachel Daly, but Everton held their nerve and Bjorn proved to be the coolest customer at Villa Park when she sent Daphne van Domselaar the wrong way from 12 yards after Kirsty Hansen felled Heather Payne.
Carla Ward’s side through everything at their visitors in the hope of finding an equaliser but the visitors showed their character to secure a priceless three points.
And Sorensen was glowing in his praise for his side’s efforts.
“I think we have a strong mentality. We score a really good goal and they score almost straight away after that. Rachel Daly is deadly and you have to be on it and for a moment we weren’t, but we showed the character to come back into the game and in the end we seen it out, even though they were throwing everything at us.
“I am super happy and very proud of the girls. With injuries and everything that has been thrown at us. Even today, we still had to manage players. (Nathalie) Bjorn couldn’t play the full 90, Karen (Holmgaard) couldn’t pay the full 90 so we had to overcome that challenge. And we still have key players that are out.
“It was a scrappy game but they are a really good team and we kept them to a minimum of chances, then we created some chances. It was long six minutes of overtime but we got through it and I’m super happy.”
Everton were the quicker of the two sides to settle and created the better of the first-half chances. Katja Snoeijs was found by Payne on 10 minutes but the Dutch striker’s shot was tame and easy for van Domselaar to collect.
The Villa stopper had to work harder for Snoeijs’ second effort though, making a finger-tip save to keep the sides level.
Daly had the hosts’ best chance of the half, but her scuffed shot was straight into the hands of Courtney Brosnan.
Everton began the second half as they had the first and were deservedly rewarded when Payne delivered a deep cross that Sara Holmgaard whipped back across the face of goal only for the unfortunate Patten to get in the way and divert into her own net.
The joy was short lived for the visitors though, as 39 seconds later Daly met Hanson’s low cross with a first-time effort to draw the sides level.
The Blues refused to let this dampen their spirits and went back after Villa.
It would be substitute Bjorn who would have the final say. Payne was clattered by Hanson in the corner of the box with the referee in no doubt it was a penalty.
And the Swedish international’s cool finish deservedly restored Everton’s lead with just over ten minutes of normal time remaining.
Brosnan, who’d had very little to do up until that point, then took centre stage to deny former Blue Simone Magill, and Kenza Dali in the latter stages as the Blues enter the international break on the back of a morale-boosting win over last season’s fifth-placed team while climbing up to eighth in the table, level with Leicester City.