No need to do that, wp_update_post() does that for you.
Are you sure this doesn’t work for you?
I see wp_update_post() calls wp_insert_post() and in that function $post_modified and $post_modified_gmt get assigned the current time. When I was testing I decided to check the record in the db and for some reason – the post modified date wasn’t saved. I had to force it inwp_fee_post to get it to work.
For the modified date to get assigned a new current date and time, this condition in wp_insert_post has to be true
if ( $update || '0000-00-00 00:00:00' == $post_date )
else it gets assigned the post creation date (which seemed to be what was happening).
All I can think of is my updated post wasn’t seen as an ‘update’ for some reason. It could well be my dev install playing games.
I’ll let you know once I investigate more.
Maybe you didn’t modify anything? I’d have to look at it.
The modifications went through, I checked that too. It was just a text update to the content.