Let's start with a small note: The `power` parameter in 

    func powerDigitSum(x:Int, var power:Int) -> Int { ... }

need not be variable, so you can remove the `var`.

You use arrays to store "large integers", and the *most* significant digit is
stored in the first array element (at index 0). As a consequence, the arrays
are reversed in `infMult()` and the result is reversed again.

It would be easier to store the *least* significant digit at index 0 of the
arrays. This simply means that you remove all `reverse()` calls in
`infMult()` and `intToIntArray()`.

This reduces the computation time slightly from 0.027 to 0.02 seconds on my
computer.

Another improvement would be to store more than one decimal digit in each
array element. On the OS X platform, `Int` is a 64-bit integer, so that
you can safely store 8 decimal digits in the array elements without
risking an overflow when multiplying two "large digits".

So you would define

    let BASE = 100000000

replace all occurrences of `10` by `BASE` in your code, and change 
`powerDigitSum()` to

    func digitSum(var x : Int) -> Int {
        var result = 0
        while x > 0 {
            result += x % 10
            x /= 10
        }
        return result
    }
    
    func powerDigitSum(x:Int, power:Int) -> Int {
        let powerSum = infPow(x, power)
        let result = reduce(powerSum, 0) { $0 + digitSum($1) }
        return result
    }

This reduces the computation time to 0.011 seconds.

The greatest performance improvement can be achieved by using a better
exponentiation algorithm in `infPow()`, such as [Exponentiation by squaring](http://en.wikipedia.org/wiki/Exponentiation_by_squaring) (see also https://codereview.stackexchange.com/a/70197/35991
for a nice explanation).

In this context this would look like

    func infPow(x:Int, var power:Int) -> [Int] {
        
        var result = [1]
        var square = intToIntArray(x)
        
        if power > 0 {
            if power % 2 == 1 {
                result = infMult(result, square)
            }
            power /= 2
        }
        while power > 0 {
            square = infMult(square, square)
            if power % 2 == 1 {
                result = infMult(result, square)
            }
            power /= 2
        }
        return result
    }

This reduces the computation time to 0.0002 seconds.