The veteran seamer overtook former England bowler Graham Onions to claim the record in a comfortable LV= Insurance County Championship win over Worcestershire.
The 33-year-old claimed his 528th first-class wicket for the club by removing Jack Haynes, having matched Onions’ county total in the first innings, and he was visibly moved by the milestone, waving to his dad who had been following the game in the car park with spectators not allowed into the Emirates Riverside.
Rushworth said: "I could not be any prouder, especially with my dad in the car park as well.
"I was very emotional, I don't think I've ever been as emotional as that on a cricket pitch.
"I've played in Lords' finals and a Championship win, but that tops the lot.
"It has been on my mind and you could probably tell with the spells on Saturday night and Sunday morning. Other milestones have not entered my mind before, but because this one was so big and it has been close for a while, it was getting to me.
"To get it done, I can get back to bowling without worrying and winning more games for Durham."
Worcestershire were dismissed for 164 as Rushworth finished with four for 52 and Mark Wood and Brydon Carse were similarly impressive with three and two wickets apiece respectively to finish off a 258-run success.
The emphatic victory moves Durham into second place in Group 1 of the County Championship, three points behind Essex.
Daryl Mitchell passed 50 for the third time this season in making 62 for the visitors.
But there was little Worcestershire resistance as Rushworth found his rhythm and the record-breaking wicket prompted emotional scenes among his team-mates and a salute to his dad in the Riverside car park, before the two men were finally able to celebrate together once the game had been finished.
Worcestershire coach Alex Gidman: "We were outplayed by a better team this week. They played a lot better than us in their home conditions and we have to take it on the chin.
"Their bowling attack is as good as we've seen this season.”