Sorting an Array of JavaScript Objects a Specific Order (using existing function)

Just use indexOf to convert the key to the correct order:

var order = ["c", "a", "b", "d"];
_.sortBy(arr, function(obj){ 
    return _.indexOf(order, obj.key);
});

Fiddle

If there are a lot of keys, then it would be advantageous to make a hash-map out of the array, like:

var order = ["c", "a", "b", "d"];
var orderMap = {};
_.each(order, function(i) { orderMap[i] = _.indexOf(order, i); });

This makes the key-sorting lookup constant time rather than O(n). (Fiddle)

Great answers provided so far. Thought that the following may also be an alternative solution in plain JS:

var arr = arr.sort(function(a,b) {
    return order.indexOf( a.key ) - order.indexOf( b.key );
    //for the sake of recent versions of Google Chrome use:
    //return a.key.charCodeAt(0) > b.key.charCodeAt(0); or return a.key.charCodeAt(0) - b.key.charCodeAt(0);
});

var arr = [
    {
        key: "a",
        value: 42
    },
    {
        key: "d",
        value: 28
    },
    {
        key: "c",
        value: 92
    },
    {
        key: "b",
        value: 87
    }
];

var order = ["c", "a", "b", "d"];

console.log( 'Original: ', JSON.stringify( arr ) );

var arr = arr.sort(function(a,b) {
      return order.indexOf( a.key ) - order.indexOf( b.key );
});

console.log( 'Ordered: ', JSON.stringify( arr ) );

const obj = [
    {
        key: "a",
        value: 42
    },
    {
        key: "d",
        value: 28
    },
    {
        key: "c",
        value: 92
    },
    {
        key: "b",
        value: 87
    }
]


const sortList = ["c", "a", "b", "d"];
    
    
const sortedObj = obj.sort((a, b) => {
    return (
        sortList.indexOf(a.key) - sortList.indexOf(b.key)
    );
});

console.log(sortedObj );