Saul's stunner gave Atleti the lead, the midfielder picking out the top corner with a sensational long-range drive that lit up a quiet first half at the Wanda Metropolitano.
When Diego Costa turned in a rebound after Antoine Griezmann was denied by Guilherme immediately after the restart, the result was effectively set in stone.
Atletico, winner of the Europa League in 2010 and 2012, has won its last six home games in all competitions without conceding a goal after easing to another comfortable victory, secured by Koke sweeping home Juanfran's cutback.
Russian Premier League leader Lokomotiv - which failed to test goalkeeper Axel Werner on his debut - will hope it can battle back into the tie on home soil in next week's second leg, but its chances of progressing appear slim.
Angel Correa's eighth-minute shot was blocked after a clever Griezmann one-two created space, but using Juanfran on the overlap was perhaps a better option.
Vladislav Ignatjev sliced wide when Manuel Fernandes held the ball up well, Koke offering Guilherme a comfortable save from a curling 25-yard strike at the other end.
But Guilherme could do little about Atleti's next effort, as Saul found the top corner from 30 yards in the 22nd minute.
With no Lokomotiv players closing the midfielder down, Saul advanced into space and thundered an unstoppable left-footed drive into Guilherme's top-right corner.
More slack Lokomotiv defending should have led to a second for Atletico, but after robbing Guilherme wide on the left flank when the goalkeeper wandered out of his area to collect a loose ball, Griezmann could only roll his finish wide of the open goal.
Aleksey Miranchuk was then booked for simulation after diving over Jose Gimenez's challenge in an attempt to win a penalty.
Atleti had struggled to create chances before the break but they doubled their lead within two minutes of the restart, Costa scoring his sixth goal since rejoining from Chelsea in January.
Saul's cross found Griezmann, but while Guilherme did well to get down to his right to push the shot away, Costa was on hand to hold off the defender and convert the rebound.
Lokomotiv had lost only one of their last nine European away fixtures but Yuri Semin's side appeared to lack belief in their chances of knocking out the tournament favourites.
Costa's penalty appeals were rejected by referee Jakob Kehlet after Vedran Corluka blocked his shot with an arm, but Atleti was cruising.
Simeone was able to rest attacking trio Griezmann, Costa and Correa in the closing stages and Mikhail Lysov forced a rare easy save from Werner with 12 minutes to go.
Koke completed the scoring with a neat first-time finish after Juanfran won the ball deep in Lokomotiv territory and put a low cross on a plate for the captain.
Atletico may have been dealt a blow in the LaLiga title race with a 1-0 defeat at Barcelona on Sunday, but they will be hard to stop as they hunt a record-equalling third Europa League title.