After edging past Norway 2-1 on Saturday, Morata's double at the Ta'Qali stadium gives Spain two wins from two in Euro 2020 qualifying and the perfect start in Group F.
Three goals in two games and another couple ruled out by VAR mean Morata looks a player revived since his January loan move from Chelsea.
Atletico's win means that the gap to leaders Barcelona is now seven points as they stayed five points ahead of Real Madrid.
The striker, who had a disappointing time at Stamford Bridge, passed his medical on Sunday, the Spanish side, his first club, said in a statement on its website.
Morata was shown leaving Atletico's medical clinic on Sunday morning, with the 26-year-old giving a thumbs up and telling reporters, "everything has gone well".
Two goals in the space of 10 minutes in the second half from the previously misfiring Morata, settled the tie for Chelsea.
The visitors were stronger than their relegation-threatened hosts in every department and perhaps the only disappointment for Sarri was that they failed to underline their dominance with further goals
Spain striker Morata, without a goal since August 18, wasted a terrific chance in the first half at Stamford Bridge but atoned with a sharp finish on 70 minutes to put Chelsea ahead.
Morata, 25, scored freely in the first few weeks after joining Chelsea last year but has appeared short of confidence recently. He has scored once this season, in August's win over Arsenal.
The Stamford Bridge club are top of the Premier League table after five wins out of five but the fixture list has been relatively kind to them so far.
Two more Chelsea players also missed out as Marcos Alonso and Cesc Fabregas were not included in the 23-man group.
Lukaku has now scored 22 times in all competitions since completing a £75 million move from Everton in July.
Conte is relieved to have options again up front in Olivier Giroud and fit-again Alvaro Morata ahead of what the Italian says is a "massive" few weeks for Chelsea.
Alvaro Morata struck his 10th goal of the Premier League campaign as Conte's side to within one point of second-placed Manchester United.
Chelsea cruised to a 4-0 victory at West Bromwich Albion in the Premier League with two-goal Hazard leading the way.