The South Americans also scored tries through German Kessler, Santiago Arata and winger Bautista Basso as they claimed a fourth World Cup victory in their history with one final pool match against the All Blacks to come.
"The players are incredible, I am very proud of them," said Uruguay coach Esteban Meneses.
"Namibia are a very tough team in the contact. They have very fast backs. We made the difference in the lineout, maul and scrum."
Namibia made a great start with a try from Gerswin Mouton in the opening minute and led 20-12 at the break but were unable to sustain their level in the second half and fell to a 26th World Cup defeat going back to their debut in 1999.
Neither team had any hope or expectation of making it to the quarter-finals from a tough pool A but there was still plenty to play for in front of a crowd of 49,432 at OL Stadium.
Uruguay had troubled France and Italy but were still looking for a win to confirm their progress, while Namibia were desperate to finally end their winless streak after big losses to the pool heavyweights.
As expected, Uruguay ran the ball from their first lineout possession but a wild pass left winger Mouton with the simple task of plucking it up and racing 60 metres to score.
JC Greyling got into the act on the other wing 10 minutes later, freed up by a pass that looked a little forward to score in the left corner and give Namibia a 14-0 lead.
Uruguay roared back and showed forward muscle of their own on the Namibian line in the 19th minute, creating space for Amaya to bump his way over a tackler and touch down.
Namibia five-eighth Tiaan Swanepoel slotted a penalty to extend the lead a few minutes later but the Uruguay pack made the next entry to the scoresheet by rolling a maul over the line for hooker Kessler to touch down.
Swanepoel added two penalties either side of the break to extend the lead to 23-12 but Namibia soon lost prop Johan Coetzee to a yellow card and Uruguay capitalised with two fine tries in five minutes.
Amaya scored the first before halfback Arata weaved his way 40 metres through the Namibian defence to touch down under the posts.
Namibia skipper Tjiuee Uanivi and replacement prop Desiderius Sethie were shown yellow cards just after the hour mark, which marked the end of their hopes.
Uruguay winger Basso touched down from a cross-kick in the 66th minute, just before the referee confirmed Sethie's offence had been upgraded to a red card.
The Namibians had a right to be fatigued in their fourth match in 19 days but showed no signs of flagging as Swanepoel added another penalty to make it a seven-point game again.
Uruguay replacement Felipe Berchesi kicked a penalty in the 74th minute, however, and the South Americans held on for victory despite having flanker Eric Dosantos yellow-carded.
