Before the draw was announced, the Town chief had spoken of an eagerness to avoid a fellow second tier side in the competition, and with seven such potential opponents still remaining, it was very much a possibility when the Hatters were first out of the hat.
But to Jones', the supporters and no doubt board and players' relief also, ball number seven was picked out by ex-Manchester United striker Andrew Cole, which saw Thomas Tuchel's finalists from last season, beaten 1-0 by Leicester City, on their to Kenilworth Road for the first time since 1991, when Richard Harvey and John Dreyer sealed a 2-0 Division One win for the hosts.
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Speaking about the draw, Jones, whose side have got past Harrogate Town and Cambridge United so far, said: "It’s fantastic for everyone involved, especially for the fans and I’m delighted for them as well.
"They missed out on two wonderful cup ties last year, Man United and Chelsea away, and now at least they get to sample a bit of that.
"It’s thoroughly deserved, we had to really play well at Cambridge, a real tricky tie as you would have seen with West Ham, Man United and Boreham Wood (going out), there are no easy games in the FA Cup.
"So to come through like we did, I was very pleased with that.
"First and foremost you want a home tie which is really good and then we didn’t really want a Championship side.
"At the time, Championship teams were probably the lowest placed so you either like to have the lowest placed side at home or a big team and we managed that.
"It's a wonderful tie, it came out nice and early so we didn’t have to get the nerves jangling."
Luton had taken on Chelsea in the competition last season, heading to Stamford Bridge in round four, as they fell 2-0 behind early on to Tammy Abraham's double.
Jordan Clark pulled one back on the half hour, beating Kepa, as after the break, Harry Cornick had a good chance saved by the home keeper, before Abraham sealed the tie with his treble late on.
That game was played out in front of an empty Stamford Bridge though, with no supporters allowed due to Coronavirus restrictions, so this time a packed Kenilworth Road should witness the tie, which being played in midweek means it will take place under the lights as well.
Jones added: "The Kenny is a great place with the atmosphere but on a midweek, I've no idea if the cameras will be there, it will be a wonderful occasion to test ourselves against a Premier League side and we will relish that opportunity.
"It’s a long way off, we have five Championship games to contend with before that but we will address it now because it’s fresh but we have big games coming up now.
"The fans have earned that.
"For all they did over lockdown and during the pandemic, they needed this game.
"We’ve given them some real special games and afternoons and evenings but this will be right up there because of the calibre of opposition."