Sanchez, who is thought to be close to a move to Barcelona after a lengthy pursuit that has involved a number of clubs, levelled for his side after Alvaro Pereira's opener.
With that in mind, they started well, with a Diego Forlan shot going wide before Liverpool's Luis Suarez wasted a great chance when he drove over after breaking through.
Forlan then saw a header chested off the line by Pablo Contreras, although the header itself hardly carried any conviction.
Uruguay went ahead in the 54th minute through Pereira, with the FC Porto man converting from close range after Suarez made his way into the box and cut back.
But Sanchez got his country back on level terms 11 minutes later, prodding home into the bottom corner after a strong run and precise pull-back from the lively Beausejour.
There was still time for Sanchez to force a save out of Fernando Muslera, but there would be no more goals.