Hackney-born teenager Watt celebrated his first goal in senior football in his 11th start for Leeds as they brushed Scunthorpe aside to stay within two points of second-placed Swansea.
He then looked ahead to a second meeting with Arsenal, whose manager Wenger decided a full season in the Championship with the Elland Road club would be beneficial to his development.
Watt, whose footballing hero is Gunners legend Thierry Henry and who is currently keeping a rung below the career ladder of great friend Jack Wilshere, played in the 1-1 draw at The Emirates and said: "My friends back at Arsenal such as Jack (Wilshere) and Kieran Gibbs have been texting me saying they are going to get revenge on us but we go into the game with a lot of confidence.
"At first I didn't think I was going to play against Arsenal but then I got myself focussed because I knew I had to have a good game and just show people that I did not want to hold back.
"Now I just want to play to the best of my ability in the replay and hopefully I can score and show everyone that I want to be a player and stay in this game for a long time.
"If I do score I won't celebrate but inside I will be happy. It would be strange to score the winning goal against a great club and a great defence and it is something to look forward to."
Watt, who has already played for England Under-16s, 17s and 19s, has made fellow 19-year-old Wilshere, who has gone on from Under-21 to full international level, something of a role model.
"I did not expect Jack to play that many games this season but he doesn't look out of place and is showing that it is not about age. It's about ability and he's getting a lot of time with the first team. If you get that chance, you have to take it.
"Everyone wants to play for a big club obviously and everyone knows Arsenal is a great club. Football changes every minute so I am going to give my all and see what happens in the summer."
Leeds manager Simon Grayson's decision to give Watt a new role – moving him inside from the left – did the trick in enabling him to break into the scoring charts.
His goal came in the 17th minute when the outstanding Robert Snodgrass, who played a hand in all three of the first half goals, headed the ball inside for Watt to produce a quick turn which left marker and Iron debutant Paul Reid on the deck before firing a sharp left-footer which the diving Joe Murphy could only help into the net.
"I've been waiting for it for some time and of course I could have had a hat-trick but it was a big win and we needed it to boost our confidence for Wednesday," said the left-footer.
"I've played in a few positions already but the gaffer said play in the hole today and get at them and gamble on the flick-ons which I did and I got a goal through it so I'm happy.
"Hopefully there is more to come along with more goals so I can help the team get promoted. We had to put the replay aside because our main is to get promoted. That is what we are focussed on."
Not one Leeds player was distracted by the prospect of playing in front of a full house on Wednesday – Arsenal are bringing just over 3,000 fans compared to the 9,000 backing Leeds enjoyed in the original tie – but they could hardly have envisaged a more comfortable warm-up.
Injury-hit Scunthorpe had won six games on the road but the next-to-bottom club, who had another debutant in Manchester City youngster Abdisalam Ibrahim, never had a chance here.
Leeds, whose proceeds from the Cup tie enabled them to bring back left-back George MCCartney from Sunderland until the end of the campaign and who continue to be linked with old boys Alan Smith and Jonathan Woodgate, had it won within 30 minutes.
Watt's sliding tackle near halfway enabled Snodgrass to thread the ball through the middle for Max Gradel to burst between two defenders and dummy Murphy the wrong way before side-footing home the second.
Then Snodgrass took a return pass from Gradel and, as two defenders slid in, saw the ball break for Bradley Johnson to hit home a deflected 25-yarder.
Luciano Becchio was rested with a sore back at the interval and replacement Billy Paynter would have netted only for Watt to inadvertently block his shot.
Leeds missed a host of chances before another substitute, Davide Somma, drilled home a late fourth after being freed by Gradel.
Michael Collins had flicked over Kasper Schmeichel but just wide and substitute Jonathan Forte was off target on the break and saw another effort balloon off Alex Bruce and onto the bar but Scunthorpe's overall response was tepid as Leeds followed up their 4-1 win at Glanford Park in October.
Hero: Robert Snodgrass
A call into the Scotland squad can not be far away for Leeds' attacking right-flank player, who set up the first three goals and gave Scunthorpe left-back Eddie Nolan, who has had a solid season, a torrid time before earning a break to the bench.
Villain: Paul Reid
Poor debut for the former Barnsley defender signed from Colchester, who also floored Max Gradel off the ball after the Leeds player had set up the fourth goal.
42nd minute: Scunthorpe's hopes of a comeback were gone when Michael Collins met a near-post cross and flicked over Schmeichel but off target.
Fred Graham: An easy afternoon for the Essex official who made no bookings in comparison to the seven issued when Leeds were at Reading.
Thoroughly professional display from Leeds who could easily have been distracted by the forthcoming FA Cup replay with Arsenal.
Quote of the day
This was far more important than the Arsenal game last week and the Arsenal game on Wednesday night, but now we've given ourselves an opportunity to concentrate on the replay with a good performance.
– Leeds chief Simon Grayson putting the Championship first.
Leeds United v Arsenal, FA Cup third round replay, Wednesday, 8.0pm.
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