Atleti were held to a 1-1 draw at Levante in midweek and their title hopes suffered a big setback against the same opponents three days later.
Morales' 12th goal of the season in the first half and Frutos' effort on the counter-attack at the death ended the leaders' run of 22 LaLiga games without defeat at the Wanda Metropolitano, giving second-placed Real Madrid the chance to reduce their advantage to only three points by beating Real Valladolid later on Saturday.
Luis Suarez struck the post with a stunning free-kick and Lucas Torreira had a goal ruled out as Diego Simeone's side raised their game in the second half, but suffered only a second loss of the season in the top flight.
Morales wasted a glorious chance to give Levante an early lead when he put a left-footed finish just wide of the far post after racing clear.
Suarez stung the palms of Levante goalkeeper Daniel Cardenas, but Atleti were punished for some slack defending when they fell behind on the half-hour mark.
Geoffrey Kondogbia was too casual when attempting to get hold of a loose ball in the penalty area and Morales capitalized, finding the back of the net with a right-footed strike that deflected off Mario Hermoso to give Jan Oblak no chance.
Ruben Rochina could have laid on a second for Morales, but his poor pass let a vulnerable-looking Atleti defense off the hook before the break.
Thomas Lemar made his return early in the second half after recovering from coronavirus, replacing the injured Jose Gimenez, before Suarez rattled the post with a magnificent long-range free-kick.
Atleti were throwing everything at Levante and Cardenas denied Joao Felix from close range before Torreira had a goal ruled out due to a push from Suarez.
Joao Felix's rasping drive was straight at Cardenas as Simeone's men continued to knock at the door.
Lemar’s left-footed volley was superbly saved by Cardenas and Suarez blazed high and wide before de Frutos rubbed salt in Atleti’s wounds right at the end, surging down the right-wing and finding an empty net from a long way out with Oblak up in search of an equalizer.