Uruguay made the Scots battle all the way and it could have been an even tighter game if the host's had a better night from the kicking tee.
Tries from Ewan Ashman, Luke Crosbie and a record breaking score from Duhan van der Merwe put Scotland 19-0 up before Uruguay replied through Santiago Alvarez and Felipe Etcheverry to make it 19-14 at the interval.
Van de Merwe passed Stuart Hogg's tally of 27 tries after playing only 41 games for Scotland.
On the 60 minute mark Uruguay replacement Manuel Diana dotted down to make it 19-19 but Patrick Harrison guided a rolling maul over the line for Scotland's fourth try of the game.
Pierre Schoeman touched down just after to ease Scotland nerves going into the final minutes.
There was still time for Kyle Steyn to go over for a try but it was chalked off due to crossing earlier in the move.
Scotland captain Rory Darge spoke after the win Montevideo:
"I think it was a great game, Uruguay were a tough side to play against.
"They made it tough for us at the breakdown which made our attack struggle to flow. We're delighted to have ground it out in the end in a fairly ugly fashion.
"It was pretty close at half-time but the bench came on and made a huge difference."