Alvaro Saborio added a goal, and Luke Mulholland scored late in the second half for Salt Lake (5-0-5).
Mark Sherrod scored twice for Houston (4-5-2), which had its three-game unbeaten streak snapped.
Morales gave Salt Lake a 1-0 lead just 15 seconds into the match, settling a Saborio pass and firing inside the upper left post.
The goal was the quickest scored in Real Salt Lake history and fourth-fastest in MLS history. New York's Tim Cahill scored the fastest goal in MLS history 7 seconds in against Houston on Oct. 23, 2013.
Morales scored again in the 17th minute to make it 2-0.
Off a corner kick, Ned Grabavoy sent a header from the upper box toward the goalkeeper's box where Morales deflected it with his right foot high into the net.
Morales added his third goal in the 89th minute on a penalty kick, delaying and then hitting his shot inside the near post as Tally Hall went to his right. Salt Lake earned the penalty kick after Hall pulled down Devon Sandoval in the box.
Sherrod cut the lead in half in the 22nd minute with his first professional goal. Off a Brad Davis corner kick, Sherrod headed it inside the near post.
Saborio upped the lead to 3-1 in the 32nd minute with a sliding header from the right box that found the net off a cross from Mulholland.
Sherrod cut the lead to 3-2 in the 56th minute, slicing a shot from the left box just inside the near post and past the hands of a diving Nick Rimando after a Salt Lake turnover.
Mulholland extended the lead back to two in the 78th minute, taking a Morales pass in the upper box, getting around a sliding Hall and sending one in the empty net from the right box.
Houston earned a penalty kick in the 35th minute as Aaron Maund pushed David Horst down in the box off a corner kick.
However, Rimando saved Giles Barnes' penalty kick attempt, diving to his right to make the stop, preserving Salt Lake's lead.
Houston played the final 63 minutes a man down after Servando Carrasco was given a straight red card by referee Allen Chapman in the 27th minute for a hard sliding tackle on Grabavoy.
Sunday’s match was likely the last time RSL will have Rimando (U.S.), Saborio (Costa Rica) and Captain Kyle Beckerman (U.S.) until after the World Cup, with all three players expected to join their respective national teams this week to prepare for the Brazil tournament. U.S. Soccer will announce its preliminary 30-man World Cup roster on Monday, with players reporting to the team’s training camp in Palo Alto, Calif. beginning on Wednesday.
Real Salt Lake will return home for its next match, hosting the rival Colorado Rapids at 7:30 p.m. MT on Saturday at Rio Tinto Stadium in the first match of the 2014 Rocky Mountain Cup.