The Canberrans will become the first Australian team to sweep all five New Zealand sides in a regular season, if they can beat the Hurricanes in Christchurch on Saturday.
But the Brumbies' looming record is being overshadowed by their recent slump, having won just two of their past six matches.
A 33-28 defeat to the Fijian Drua last round only compounded their woes, but Larkham feels the addition of Muirhead back into the starting 15 can give his side the injection needed to beat their opponents.
"The Hurricanes are top in the stats in about everything at the moment, especially attack stats," Larkham said.
"It's going to be a battle to maintain scoreboard control, and Andy will certainly give us that attacking threat.
"It was a tough decision. But Andy gives some really good leadership in the attacking game."
Muirhead was shifted to the bench after Wallabies No.15 Tom Wright made his return last Saturday night, but rather than putting Muirhead into the fullback role, Larkham moved him onto the wing.
That means Ollie Sapsford has been shifted to the bench, while Rory Scott returns to the back row replacing Luke Reimer.
Larkham is hoping the changes can provide his team with the much-needed points to keep the Brumbies' top-two aspirations alive.
"You've got to be careful about looking at a loss and having a knee-jerk reaction. We lost the game against the Waratahs, the game against the Reds, and twice against the Drua," he said.
"Across the board, apart from that Fiji game in Fiji, we've been quite consistent ... We're still chasing the top two (despite being six points behind)."
The Hurricanes will be looking to bounce back from an extra time 22-17 loss to the table-topping Chiefs and coach Clark Laidlaw has made a plethora of changes, with the All Blacks' Du'Plessis Kirifi's set for his 100th Super Rugby appearance.
Siale Lauaki, Raymond Tuputupu, Tevita Mafileo have been promoted in the front row, while second-rower Caleb Delany and No.8 Brayden Iose are also returning to the starting 15.
Both teams will be playing for the Captain Shout Cup, named after the Wellington-born Anzac soldier Captain Alfred Shout, who was awarded the Victoria Cross.
"It's something we've spoken about as a team," Larkham said.
"If you go back, the ACT side used to play against Wellington, and they played for a trophy."
