After being denied a penalty in the first half — and subsequently given a yellow card for diving — Vardy converted a 55th-minute spot kick after Jonny Evans was fouled by Adam Masina.
Flores was fired Sunday with Watford in last place in the Premier League and having won just one match in 14 this campaign.
Gerard Deulofeu and Andre Gray scored for Watford as they moved off the bottom of the standings to 18th.
Christian Pulisic scored in his second Premier League game in a row while Tammy Abraham continued his fine form as Chelsea beat Watford 2-1 on Saturday.
Manchester City earned a routine 3-1 victory against Southampton while Leicester and Everton defeated Burton Albion and Watford 3-1 and 2-0 respectively.
Watford looked headed for its first league win of the season after Abdoulaye Doucoure put the visitors ahead in the sixth minute and Tottenham once again looked short of inspiration as it struggled to find a response.
City ended up romping to an 8-0 win, falling just short of the heaviest margin of victory in the Premier League era (since 1992) — Manchester United's 9-0 win over Ipswich in 1995.
Frustration continued for Unai Emery and Arsenal as they were held by 20th placed Watford in the Premier League.
It was Arsenal's first clean sheet in an away league match this season.
Watford reached its first final in 35 years as they came from behind to beat Wolves 3-2 at Wembley.
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