A 90th-minute third from Koke then set the two-time winners well on their way to the quarter-finals.
The Spaniards had won their previous five games at Wanda Metropolitano without conceding and continued that impressive run against the Russian Premier League leaders.
Lokomotiv, playing in this stage of the Europa League for the first time, were content to sit behind the ball and try to make it difficult for Atletico to create clear-cut chances.
Although it only took the hosts 22 minutes to break this rearguard, it needed a moment of magic from Saul as he surprised Guilherme with a left-footed shot into the top corner.
The Lokomotiv goalkeeper nearly gifted Atletico a second on the half-hour mark when he wandered off his line and tried to take on Antoine Griezmann, who pinched the ball but could not slot it into the vacant net from the left byline, his side-footed shot rolling wide of the post.
Griezmann came close again two minutes into the second half when his cushioned volley was pushed away by Guilherme, with the rebound falling to Costa for the striker to steer home his sixth goal in 10 matches.
With Jan Oblak missing with a hand injury, Axel Werner made his debut for Atletico but Lokomotiv did not work the rookie goalkeeper until the 78th minute when he held on to Mikhail Lysov's piledriver.
Atletico's dominance allowed Simeone to spare Griezmann, Costa and Angel Correa in the last quarter, but the hosts still had enough on the field to extend their advantage ahead of next week's second leg.
Juanfran's high pressing earned him the ball inside the Lokomotiv half, and the full-back had the awareness to spot the run of Koke, who guided the ball inside the far post with a first-time shot from 12 yards.
ATLETICO (4-4-2): Werner; Juanfran, Gimenez, Lucas, Luis; Thomas, Saul, Correa (Torres, 75'), Koke; Griezmann (Vitolo, 67'), Costa (Gameiro, 75')
LOKOMOTIV (4-5-1): Guilherm; Ignatjev (Lysov, 53'), Corluka, Kvirkvelia, Rybus; Anton Miranchuk (Kolomeytsev, 71'), Denisov, Pejcinovic, Fernandes, Aleksei Miranchuk; Eder