Этот способ спас нас.

Because способ is a masculine singular noun, and этот has to agree with it.

• этот = masculine singular
• эта = feminine singular
• это = neuter singular
• эти = plural

So:

• этот способ = this method / this way

Since способ is masculine, этот is the correct form.

Способ usually means method, way, or means of doing something.

Depending on context, Этот способ спас нас could sound like:

• This method saved us
• This way saved us
• This approach saved us

It is a common word for a practical solution or technique.

Спас is the perfective past tense form, which usually shows a completed result.

Here it means that the action was completed: the method saved us.

Compare:

• спас = saved, managed to save, brought about the result
• спасал = was saving, used to save, tried to save, saved repeatedly/in an ongoing way

In this sentence, the idea is that the method actually worked and produced the result, so спас is the natural choice.

Because нас is the form used for us, while мы means we.

In this sentence, us is the direct object of the verb saved, so Russian uses the accusative case.

• мы = we
• нас = us

So:

• Мы спасли их = We saved them
• Этот способ спас нас = This method saved us

Russian past tense verbs are formed differently from English, and in the masculine singular they often appear with no extra vowel ending.

Here the subject is способ, which is masculine singular, so the verb is also masculine singular:

• спас = masculine
• спасла = feminine
• спасло = neuter
• спасли = plural

Examples:

• Этот способ спас нас = This method saved us
• Эта идея спасла нас = This idea saved us
• Это решение спасло нас = This decision saved us
• Эти меры спасли нас = These measures saved us

The dictionary form is спасти = to save.

This is a somewhat irregular-looking verb in the past tense:

• infinitive: спасти
• past masculine: спас
• past feminine: спасла
• past neuter: спасло
• past plural: спасли

So when you see спас, it comes from спасти.

Yes. Спасти can mean literal rescue, but it is also very commonly used figuratively.

So Этот способ спас нас could mean:

• literal: the method physically saved our lives
• figurative: the method got us out of a difficult situation
• idiomatic: this approach really bailed us out

Russian uses спасти in both serious and everyday situations.

No, Russian word order is fairly flexible because case endings show the grammatical roles.

The neutral order here is:

• Этот способ спас нас

But other orders are possible, for example:

• Нас спас этот способ
• Спас нас этот способ

These alternatives change the focus or emphasis, not the basic meaning.

Very roughly:

• Этот способ спас нас = neutral statement
• Нас спас этот способ = emphasis on us
• Спас нас этот способ = more dramatic or literary emphasis on the action/result

A simple learner-friendly pronunciation guide is:

• этот ≈ EH-tuht
• способ ≈ SPO-suhp
• спас ≈ spahs
• нас ≈ nahs

Stress:

• Э́тот спо́соб спас нас

A few useful notes:

• этот is stressed on the first syllable
• способ is stressed on the first syllable
• final consonants in Russian are often devoiced, so способ may sound a bit like sposop at the end

No. Russian has no articles.

So Этот способ already means this method / this way, and you do not need a separate word for the.

Russian expresses definiteness through context, demonstratives like этот, and word order when needed.

In Russian, demonstratives like этот normally come before the noun they describe.

So:

• этот способ = this method
• эта книга = this book
• это решение = this decision

Putting этот before the noun is the standard pattern.

Sometimes yes, depending on context, but способ is not exactly the same as solution.

• способ = method, way, means, approach
• решение = solution, decision

If the idea is a way of doing something that helped, then method or approach is better. If the wider context is about solving a problem, English might naturally use solution, but the Russian word still specifically says method/way.

The demonstrative and the past tense verb would both change to agree with the subject.

For example:

• Эта идея спасла нас = This idea saved us
• Это средство спасло нас = This remedy saved us
• Эти меры спасли нас = These measures saved us

So in Russian, both the demonstrative and the past tense verb show agreement with the subject’s gender and number.