Since the forEach is synchronous and the request is asynchronous, there is no way to do it exactly as you describe. What you can do however is to create a function that handles one item from the docs array and removes it, then when you're done processing, go to the next:
var results;
var productsToProcess;
MongoClient.connect( 'mongodb://localhost:27017/suppliers', function ( err, db ) {
  assert.equal( null, err );
  var findDocuments = function ( db ) {
    var collection = db.collection( 'products' );
    collection.find( {
      $and: [ {
        "qty": {
          $gt: 0
        }
      }, {
        "costex": {
          $lte: 1000.0
        }
      } ]
    }, {
      "mpn": 1,
      "vendor": 1,
      "_id": 0
    } ).limit( 1 ).toArray( function ( err, products ) {
      assert.equal( err, null );
      productsToProcess = products;
      getSearching();
      db.close();
    } );
  }
  findDocuments( db );
} );
function getSearching() {
  if ( productsToProcess.length === 0 ) return;
  var product = productsToProcess.splice( 0, 1 )[0];
  var keyword = product[ 'vendor' ] + ' "' + product[ 'mpn' ] + '"';
  google( keyword, function ( err, res ) {
    if ( err ) console.error( err )
    for ( var i = 0; i < res.links.length; ++i ) {
      var result = res.links[ i ];
      var obj = {
        title: res.links[ i ].title,
        href: res.links[ i ].href,
        description: res.links[ i ].description
      }
      results.push( obj );
    }
  }, processData );
}
function processData( results ) {
  MongoClient.connect( 'mongodb://localhost:27017/google', function ( err, db ) {
    assert.equal( null, err );
    // insert document to DB
    var insertDocuments = function ( db, callback ) {
      // Get the documents collection
      var collection = db.collection( 'results' );
      // Insert some documents
      collection.insert( results, function ( err, result ) {
        assert.equal( err, null );
        console.log( "Document inserted" );
        callback( result );
        db.close();
      } );
    }
    insertDocuments( db, getSearching );
  } );
}
EDIT
Moved the products from the database to the productsToProcess variable and changed the getSearching() to no longer require a parameter.