Atalanta hadn’t even recovered from conceding the first before they found themselves two goals down inside three minutes.
Hakan Calhanoglu curled in a sublime shot from the edge of the box but his effort was quickly chalked off for an offside decision, capping off a breathless opening 10 minutes.
As the half went on, the game began to settle with Atalanta finding rhythm and managing to keep possession, though Inter continued to look dangerous with every attack.
Rasmus Hojlund came closest for the visitors from Bergamo as he ran onto a through ball and fired towards goal but it was comfortably palmed away by Andre Onana.
La Dea continued to threaten as the half came towards a close and they pulled a deserved goal back after the Inter defence failed to clear a corner, and following a scramble in the box, Mario Pasalic fired the loose ball in.
Simone Inzaghi’s side were in full control once again at the beginning of the second period but this time failed to turn their dominance into goals. Calhanoglu stung the palms of Sportiello with a powerful shot from distance but the Atalanta shot-stopper managed to steer the shot away for a corner.
La Dea knew only a win would give them a fighting chance of finishing in the top four but as they pushed more men forward, they continued to look vulnerable at the back. And Inter duly punished Gian Piero Gasperini’s men with a quick counter-attack which was finished off by Marcelo Brozovic laying the ball off to Lautaro Martinez to tap into an empty net and secure all three points and a top-four spot for the Nerazzurri.
Luis Muriel added a second goal for Atalanta late on with a stunning shot from distance that flew in off the bar, a goal which saw the Colombian become the highest goal-scoring substitute in Serie A.
The win for Inter sees them rise to second place, with Lazio yet to play this game week but Inzaghi’s men continue to grow in confidence as they prepare for the Champions League final against Manchester City in two weeks.
Meanwhile, Atalanta remain in fifth but may need to secure a positive result in the final game of the campaign to confirm European football for next season.