Elliot Lee opened the scoring after four minutes with a smart finish, before Danny Hylton was dragged to the ground in the penalty area by Ryan Dickson – resulting in a straight red card for the Glovers full-back after just 20 minutes.
Hylton scored the penalty that followed, before Francois Zoko received his marching orders 12 minutes later for a coming together with Alan McCormack. The Hatters wrapped up the scoring with Hylton firing home from close range just before the break.
Town recorded their first back-to-back wins since the end of January, as they moved eight points clear of fourth place.
Jones said: “I am delighted. It’s always a tricky encounter coming here. They had a wonderful result last week where they won 6-2 away from home where it’s never an easy place to go [Coventry]. To score six is wonderful.
“So we knew it would be difficult, we thought the pitch would be a bit more difficult. But from start to finish – we’ve talked about our starts where we’ve conceded away from home early, but we were the ones who have got off to a flying start. You could see it in them, they were really at it.
“We scored a good goal, we could have scored again, Hylton had a great chance and then we got the second. Then you’re kind of thinking it’s going to be our day.
“We made a big thing of it – our starts have killed us because we score almost every game, if not every game. We give ourselves mountains to climb, so we wanted to get off to a [good] start. By scoring early and scoring first we did that.
“I thought from start to finish we were thoroughly professional in everything we did. I know some people will be disappointed we didn’t go onto score loads more goals, but it wasn’t about that. It was about getting over the line and that was thoroughly professional.”