This date function below achieves the desired effect without an additional script library. Basically it's just a simple date component concatenation in the right format, and augmenting of the Date object's prototype.
 Date.prototype.dateToISO8601String  = function() {
    var padDigits = function padDigits(number, digits) {
        return Array(Math.max(digits - String(number).length + 1, 0)).join(0) + number;
    }
    var offsetMinutes = this.getTimezoneOffset();
    var offsetHours = offsetMinutes / 60;
    var offset= "Z";    
    if (offsetHours < 0)
      offset = "-" + padDigits(offsetHours.replace("-","") + "00",4);
    else if (offsetHours > 0) 
      offset = "+" + padDigits(offsetHours  + "00", 4);
    return this.getFullYear() 
            + "-" + padDigits((this.getUTCMonth()+1),2) 
            + "-" + padDigits(this.getUTCDate(),2) 
            + "T" 
            + padDigits(this.getUTCHours(),2)
            + ":" + padDigits(this.getUTCMinutes(),2)
            + ":" + padDigits(this.getUTCSeconds(),2)
            + "." + padDigits(this.getUTCMilliseconds(),2)
            + offset;
}
Date.dateFromISO8601 = function(isoDateString) {
      var parts = isoDateString.match(/\d+/g);
      var isoTime = Date.UTC(parts[0], parts[1] - 1, parts[2], parts[3], parts[4], parts[5]);
      var isoDate = new Date(isoTime);
      return isoDate;       
}
function test() {
    var dIn = new Date();
    var isoDateString = dIn.dateToISO8601String();
    var dOut = Date.dateFromISO8601(isoDateString);
    var dInStr = dIn.toUTCString();
    var dOutStr = dOut.toUTCString();
    console.log("Dates are equal: " + (dInStr == dOutStr));
}
Usage:
var d = new Date();
console.log(d.dateToISO8601String());
Hopefully this helps someone else.
EDIT 
Corrected UTC issue mentioned in comments, and credit to Alex for the dateFromISO8601 function.