The combative forward was introduced as a substitute for the hosts, scoring the second half penalty which levelled the scores.
Troy Deeney scored from the spot in the 71st minute to cancel out Per Mertesacker's opener after Gunners right-back Hector Bellerin was ruled to have fouled Richarlison in the box.
However, in Arsenal, they faced yet another test of their mettle under new manager Marco Silva with the Gunners entering the game on a seven-game unbeaten streak.
Mertesacker does not know if the penalty was worth it, but bemoaned the fact that Arsenal became wasteful, as Cleverley scored a late victor. Whenever I play against Arsenal, I'll go up and think, "Let me whack the first one and see who wants it".
'I don't think there are many teams, top teams, that had the chance Ozil had and be so naive, so nonchalant with it, ' he said after Watford climbed to fourth in the table.
"For me, as a player, I just think happy days". I nodded it down, the crowd got up - "yeah we've got somebody who can win it" - and they all just backed off.
"If you like to play to win a game, and if you have one clear idea for the players, I can not change this idea in one week because I will play against Arsenal, or I will play against Chelsea or Man City. That's my strength - if you're going to let me do my strength against you, you're going to have a tough afternoon".
"Of course the players know that it is important to have the humility to understand what type of team we'll play against".