Word/phrase for when an incorrect approach leads to an unexpectedly great result

Question

Related question on Chinese.SE

There is a phrase ("歪打正着" in Chinese and "怪我の功名" in Japanese) which roughly means "do the wrong thing but achieve the right result anyway". Is there a similar phrase or idiom in English?

Examples:

• (From the related question): The subject brings a gift to a friend but the friend wasn't present. When the subject tried again on another day, the friend was present, but - unknown to the subject - it was also the friend's birthday, so the gift became a birthday gift too.
• When you lose your job/lover but this leads you to find a much better one

Some translations available online are "score a lucky hit" or "hit by a fluke" but I feel these do not capture the incongruity between approach and outcome.

Compare this with situational irony, which is often used when the aim or intent is good but the outcome is incongruously bad.

Answer 1

For your examples, the word serendipitous would fit:

serendipitous adjective
occurring or discovered by chance in a happy or beneficial way:
a serendipitous encounter

serendipity noun [mass noun]
the occurrence and development of events by chance in a happy or beneficial way:
a fortunate stroke of serendipity

[ODO]

Apparently the word is a coinage:

1754: coined by Horace Walpole, suggested by The Three Princes of Serendip, the title of a fairy tale in which the heroes ‘were always making discoveries, by accidents and sagacity, of things they were not in quest of’