The Chiefs clocked up their third successive top flight victory on Saturday, as 11 points from the boot of Henry Slade and Chudley's late try helped secure a 16-6 victory against their nearest and dearest.
Exeter's success helped to propel Rob Baxter's side back into the top three with just six rounds of domestic league action remaining.
And next up for the Westcountry outfit is another home encounter against winless London Welsh this Saturday (3pm).
Having defeated the Exiles comfortably 52-0 on the opening day of the season, Chudley says it's imperative he and his team-mates maintain their momentum with another big display.
“We are absolutely delighted. We had played them nine times (in the Premiership) and hadn’t beaten them once so it was massive to get this monkey off our back,” said the 26-year-old back.
“Also, in terms of where we are and building towards the goals we want to achieve, it is a massive result. We have a massive game next week though so we need to just focus on that, work really hard and bang in another win.”
The Chiefs, however, will come into this latest match-up brimming with confidence having recorded a notable scalp in seeing off Bath for the first time in ten attempts.
Chudley paid credit to the part Bath played in a hard-fought encounter, but admitted it was the fighting spirit and control of the Chiefs which came to the fore come the end.
“It was a tough game but we had some tough boys who stood up and we got the result,” he said. “We didn’t start particularly well and we had a few words at half-time about really attacking the game and really taking it to them.
“Fair play to Bath, they stood in front of us for 80 minutes and gave us a really tight game. Bath are a very, very good team – we know they have a few boys away but the boys they have in their positions are equally good. We knew we had a massive game, but I am so proud of the boys that we got the result that we wanted.”