Searching file for string surrounded by two other known string?

Question title may be kinda vague, but heres what im attempting to do.

I have a html file locally on my server which is changing fairly regularly. It has multiple occurrences of:

<p>Jumble of random text</p>
<p>More text</p>

And so on...

I want to be able to sort through all the different jumble of random text's till it finds the one I am looking for, for example 'random', which could be anywhere in the file. Then I want a variable assigned to

Jumble of random text

Everything between the:

<p> and </p>

So far I have this:

echo grep -i 'random' search.html | grep -o -P '(?<=<p>).*(?=</p>)' search.html

Which works to an extent, however it is finding the first occurrence and the last occurrence of the paragraph tags, therefore giving me a huge output of meaningless data, ie in this case:

Jumble of random text
More text

How can i get it to just return:

Jumble of random text

Getting very confused, very fast.