Morris, a 20-year-old Stanford University sophomore who got his first starting nod for the USA, opened the scoring in the 49th minute and Agudelo, a second-half substitute making his first appearance for the US after a three-year absence, doubled the score with a 72nd-minute strike.
Their efforts gave the Americans their second victory of the calendar year, and improved Jurgen Klinsmann's unbeaten record against regional rivals Mexico as US coach to six games.
The match at the Alamodome gave Klinsmann another chance to assess players in the build up to the CONCACAF Gold Cup, the regional championship that will be played July 7-25.
Mexico are also preparing for the Gold Cup, and for the Copa America June 11-July 4.
Morris provided some moments of encouragement in an otherwise dull first half between two teams below full strength.
Mexico had the best opportunity of the first half, when five minutes before the break Gerardo Flores's cross to the near post was sent wide by Eduardo Herrera.
Minutes into the second half, US World Cup veteran Michael Bradley played a forward pass to Gyasi Zardes.
The Los Angeles Galaxy striker let the ball run and Morris was first to react, taking a direct touch into the Mexico box before sliding a right-footed shot past Mexico keeper Cirilo Saucedo.
Bradley also played a key role in the host's second goal.
The Toronto FC midfielder sent a long ball to the corner of the box where Agudelo was arriving. The 22-year-old turned toward the goal, floating inside and belting a low shot that beat Saucedo at the near post.
Mexico made a late push to pull back a late goal, and nearly capitalized on some late confusion in the US penalty area.
But substitute goalkeeper William Yarbrough came off his line to collect the ball and preserve the 2-0 scoreline.