Stumbled over greeting and put up with touching (3,4)

'stumbled over' is the definition.
(to hit upon something is to stumble across it)

'greeting and put up with touching' is the wordplay.
'greeting' becomes 'hi' (hi is a kind of greeting).
'and' says to put letters next to each other.
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'with' is a charade indicator (letters next to each other).
'touching' becomes 'on'.
'put' written backwards gives 'tup'.
'hi'+'tup'+'on'='HIT UPON'