Former Basel man Leutwiler, 23, has been given the chance to impress in the absence of Jason Steele, who is at the Olympics with Team GB.
Curtis Main put Boro ahead in the first half at Brunton Park, but Lee Miller's header levelled for the Cumbrians. Scot Cameron Park tucked in Marvin Emnes' pull back 25 minutes from the end to secure victory for Mowbray's men.
Boss Mowbray told the club's official website: "There's potential for us to bring in two goalkeepers. I haven't seen anything to suggest Leutwiler can't do it, but it's a decision I have to think about carefully.
"Your gut reaction is to go for a 30-year-old with experience for when the real matches kick in, but then I think `would he have been as agile as Jayson at Carlisle' for example.
"He made some great saves early on and was dynamic. I haven't seen many negatives."