Those victories were desperately needed after Kirk's side were somewhat subjected to a baptism of a fire in the opening weeks of the Women's Super League season, where they lost 4-0 to both Chelsea and Manchester City.
Everton have made no secret of their ambitions to break into the Champions League in the near future and this weekend's game against Arsenal marks a perfect opportunity for Kirk's side to lay down a marker against the WSL's early leaders.
Arsenal, though, have one of the most dangerous attacks in the league, which includes none other than Dutch international Miedema, who recently passed the 100 goals mark for the Gunners.
Speaking to talkSPORT, the Everton boss said: "I'm not quite sure how you stop Viv. You need to be aware in the box. Your centre-backs need to be aware of where she is and I think she seems to be moving a little less in terms of roaming around.
"She had bit more of a free licence under Joe [Montemurro, former Arsenal Women boss] I think to go and find pockets of space on the pitch and then she would appear on your blind side in the box because she'd been 70-yards from goal two minutes earlier.
"She's playing a little higher and a little bit more central and I actually think that can help us. We have knowledge of her whereabouts.
"She's the best striker in the world, in my opinion. When you're playing against one of the best strikers in the world, you need to know where she is. Free space doesn't score goals, but Viv does and you need to know where she is.
"Let's prevent the chances and lets prevent them from getting the ball and lets prevent them from being dangerous. Mitigate some of the risks. Ultimately, if it gets to that stage, you've got to know where she is in the box, or she'll punish you.
"We have a really good changing room. I think the players have shown quite a lot of resilience because they have taken a few knocks over the first couple of weeks. They've taken a lot of criticism.
"I think it was quite obvious the pressure we were playing under against Birmingham and they came through it really well and they've come out the other side with a couple of results. Now, it's about trying to keep that momentum."