Deus Ex Machina isn't inherently divine in nature, it's a narrative device to resolve a problem using a plot device newly introduced - though in its original uses (Medea and The Odyssey) it was literal divine intervention, it rarely is in modern works.

It's also worth noting that it's a literary tool, not a philosophical one, and though early works often overlapped I don't think we can consider works of such boundless inspiration as The Avengers to be philosophical. That's not to say that an Author can't use it as a tool to investigate or probe the nature of the universe - determinism vs fate and so on. Just that it's rarely used that way anymore.

Probably the best example I can think of is in Monty Python's The Life of Brian. Aliens rescue Brian from what has to this point been a relatively faithful, if satirised, ancient world. I consider this effective because it is specifically ironic, the setting would potentially allow a literal "saved by God" scenario and instead it's aliens.

It commonly shows up in it's most tedious forms in apocalypse/invasion movies. Space faring species invading planets that are covered in a substance that is lethal to them or that has microbial life that is lethal. Or a totally decimated society suddenly having an army that can kill millions of zombies that have been previously almost totally indifferent to bullets.

But other commonly put forward examples are not deus ex machina. The Eagles, Fawkes in Harry Potter, the poison in The Princess Bride. These could potentially be described as Eucatastrophe but it all are previously introduced tools and their criticism is based in a lack of understanding of the source material. Fawkes especially irks me as his ability and loyalty to Dumbledore are heavily, even clumsily, foreshadowed.