multi subdocument update in Mongo subdocument arrays

I am trying to update multiple subdocuments within a Mongo collection, where there may be multiple matches within the same collection. Unfortunately, it is only updating the first subdocument within each document that has a match.

Here is the code:

var mongoose = require('mongoose');

mongoose.connect('mongodb://127.0.0.1/touchbits');

var PartsSchema = new mongoose.Schema({
        type: String
        , partNbr: Number
    });

var ProductSchema = new mongoose.Schema({
        sku: { type: String, unique: true }
        , parts: [PartsSchema]
    });

Product = mongoose.model('Product', ProductSchema);

var cigars = new Product({
        sku: 'cigar123',
        parts: [{type: 'tobacco', partNbr: 4}, 
                {type: 'rolling paper', partNbr: 8}, 
                {type: 'tobacco', partNbr: 4}]
    });
var cigarillo = new Product({
        sku: 'cigarillo456',
        parts: [{type: 'tobacco', partNbr: 4}, 
                {type: 'crush paper', partNbr: 12}]
    });

cigars.save(function(err, product1) {
        if(err) { console.log("err1: " + err); return err; }
        console.log("saved: " + product1);
        cigarillo.save(function(err, product2) {
                if(err){ console.log("err2: " + err); return err; }
                console.log("saved: " + product2);
                Product.update({ "parts.type": 'tobacco' },
                               { $set: { "parts.$.partNbr": 5 } },
                               { multi: true },
                               function(err, numAffected) {
                                   if (err) { console.log("err3: " + err); return err; }
                                   console.log("records updated: " + numAffected);
                                   Product.find({}, function(err, docs) {
                                           if (err) { console.log("err4: " + err); return err; }
                                           console.log("updated data: " + docs);
                                           Product.remove(function(err) {
                                                   if (err) { console.log("err5: " + err); return err; }
                                                   process.exit();
                                               });
                                       });
                               });
            });
    });

Then when I run it, I get the following results:

saved: { __v: 0,
  sku: 'cigar123',
  _id: 51c9229b7fe80ef71e000002,
  parts: 
   [ { type: 'tobacco', partNbr: 4, _id: 51c9229b7fe80ef71e000005 },
     { type: 'rolling paper',
       partNbr: 8,
       _id: 51c9229b7fe80ef71e000004 },
     { type: 'tobacco', partNbr: 4, _id: 51c9229b7fe80ef71e000003 } ] }
saved: { __v: 0,
  sku: 'cigarillo456',
  _id: 51c9229b7fe80ef71e000006,
  parts: 
   [ { type: 'tobacco', partNbr: 4, _id: 51c9229b7fe80ef71e000008 },
     { type: 'crush paper',
       partNbr: 12,
       _id: 51c9229b7fe80ef71e000007 } ] }
records updated: 2
updated data: { sku: 'cigar123',
  _id: 51c9229b7fe80ef71e000002,
  __v: 0,
  parts: 
   [ { type: 'tobacco', partNbr: 5, _id: 51c9229b7fe80ef71e000005 },
     { type: 'rolling paper',
       partNbr: 8,
       _id: 51c9229b7fe80ef71e000004 },
     { type: 'tobacco', partNbr: 4, _id: 51c9229b7fe80ef71e000003 } ] },{ sku: 'cigarillo456',
  _id: 51c9229b7fe80ef71e000006,
  __v: 0,
  parts: 
   [ { type: 'tobacco', partNbr: 5, _id: 51c9229b7fe80ef71e000008 },
     { type: 'crush paper',
       partNbr: 12,
       _id: 51c9229b7fe80ef71e000007 } ] }

Notice that the second 'tobacco' record in the 'cigars' document still has a PartNbr of 4 instead of 5. Does anyone know how to change the update to update all the subdocuments within an array that match the query condition?