Here, Sports Mole analyses how the points were won in the Spanish capital.
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On target: 10
On target: 3
Was the result fair?
With Astana opting to leave so many of their best players back in Kazakhstan, the result was arguably settled before a ball was kicked. The visitors did not turn up looking for anything other than a defeat. Their primary concern was avoiding a humiliation and such an unambitious approach made for a relatively dull spectacle, despite the four goals.
Atletico Madrid's performance
It was ever so easy for Diego Simeone and co tonight. Then again, it was always going to be a walk in the park. It was one-way traffic for the first 20 minutes or so, but a wall of yellow shirts was proving difficult to breach. It was a case of Better Call Saul, with the 20-year-old opening the scoring on 23 minutes when his exquisite flick to meet Yannick Carrasco's cross was enough.
It had been coming, and another one came along six minutes later when the much-maligned Martinez - who had earlier missed a sitter from point-blank range - atoned for that error by turning and scuffing home from 12 yards. Only Simeone had a bigger smile on his face, having defended the misfiring striker regularly following an inauspicious start to his Atletico career.
The Argentine coach pulled off Tiago for Torres at the break in an inspired change, with the youngster clipping over Nenad Eric on 63 minutes for the third. It was another Torres in Fernando who could, and should, have fattened the advantage, but the former Liverpool striker spurned two glorious chances as his wait for a 100th Atletico goal goes on.
He thought that he had it right at the end when he looked certain to tap home Gabi's cross, but Dedechko slid in to add a fourth. Bigger tests lie ahead for the Rojiblancos, but Atleti - who reached the final in 2014 - are now top of Group C and a last-16 place beckons.
By virtue of the fact that Stanimir Stoilov left eight of his heavy hitters at home, it could be argued that winning was not a priority for the visitors. In fact, it could be argued that a new-look Astana side had no intention of even scoring.
At times, Stoilov had no fewer than five centre-halves lined up in the box, with wingers Aleksei Schetkin and Foxi Kéthevoama effectively operating as full-backs. With a seven-man defence, their mandate was simple: return to Kazakhstan with as much respect as possible, though the way they went about it should have the opposite effect.
Stoilov and his troops had to negotiate three qualification ties before booking their seat at the big table. Given how treacherous their route into the competition was, this was bitterly disappointing. They are the only Kazakhstani team in history to reach the Champions League proper, but the flag that they flew was a white one and any fans loyal enough to make the 4,000-mile trip deserve to have their travel expenses reimbursed.
Sports Mole's man of the match
Yannick Carrasco: There were few candidates in truth, but none stood out more than the ex-AS Monaco winger, who impressed in both halves and set up the first goal.
On another night, Martinez could have had a hat-trick. The Colombian, who scored one, missed a gilt-edged header midway through the first half. It was an error that would look poor on a Sunday League stage let alone the Champions League.
Aleksei Kulbakov did not have much to do, but Yeldos Akhmetov - recipient of the game's only yellow card - tested him following a studs-up challenge on Juanfran early in the second half. There would have been few complaints had the Bulgarian brandished a red card instead.
Atletico Madrid: Simeone's side are back at the Vicente Calderon on Sunday for the visit of fellow Champions League outfit Valencia.
Astana: They travel away to Kairat Almaty on Sunday afternoon.