Two penalties from Alex Davies helped a much-changed Welsh outfit reach half-time level at 6-6, and another penalty early in the second half briefly nudged the visitors in front.
But Grenoble, whose first half points had come from two Clement Darbo kicks, responded with a converted try by Vincent Campo, and Andrew Farley scored a second late try for the hosts to confirm victory.
The result leaves London Welsh in third place in Pool Five with just one win from three games.
Grenoble top the group ahead of Stade Francais, who were due to play Cavalieri on Saturday.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.