The centre-back was on the scoresheet twice, as was Kirsty Howat, as the Light Blues put on a strong display in front of a home crowd at Broadwood Stadium.
Speaking to RangersTV at full-time, Davison praised the way the squad handled early second-half pressure from Hibs to finish off the game.
She said: “I think it was a really good team performance, obviously coming off of the cup final against them we knew that they were going to be hungry to come at us so I think the team did really well to handle that pressure and to stay composed and take the three points.
“It was really important to not let them get back into the game at all so it was just about staying calm and they came out running right at us but to be able to handle that pressure and then flip it on them was really good.”
Davison got on the end of two corners from Tessel Middag as the American-born defender netted her first two goals of the SWPL season, while also playing a key part at the other end of the pitch in another clean sheet for Malky Thomson’s side.
Reflecting on her own contribution this evening, she said: “I am happy, I haven't scored many goals this season, so I think we have done a good job generating set pieces and I am just happy to be able to contribute to the team.
“We have a lot of players who are very threatening in the air so it is just about taking advantage of those opportunities and having so many runners going into the box odds are one of us are going to get on it so I am just pleased that we are finishing our set pieces.
“The whole back-line and the team takes a lot of pride in keeping the shutout and keeping the goals against us this season to a minimum so again I am really proud of the group staying organised and keeping the ball out of the net.”
Looking ahead to Sunday’s Scottish Cup match against Rossvale, Davison continued: “The cups are always really fun, so we just have to carry the momentum from the last couple of games into that and just keep going and keep winning.
“Looking at the numbers we are one of the fittest teams and you can see it on the field we have a lot of depth on the team, so it has been nice to manage numbers and just keep fresh legs going constantly.
“Our fitness is definitely paying off and that is why it is so important to do the work and we will just continue to get stronger.”