Bakary Sako scored either side of Nouha Dicko's strike to give Wolves a 3-0 half-time lead before Leon Clarke smashed in his first for the club in injury-time after Michael Smith had pulled one back.
The win ensures Jackett's side have won nine in a row for the first time in their history and beat their previous best of 1988.
Jackett said: "It's a great feeling to get a new club record.
"It's a terrific achievement by the players, but our main motivation for the season is to get promoted.
"If the club record comes within that, it will be an added bonus. Our first-half performance was as good as we've played.
"It was some excellent football and some clinical finishing. We could perhaps have had more goals.
"In the second half we fell away and we tried to manage the game, but it didn't work like that."
Wolves oozed class as they clinically dismantled the Robins with three goals in 35 minutes to remain top of the table.
Sako glided in unmarked at the far post to open the scoring and shortly after James Henry had rattled the Swindon upright, the Wolves striker turned creator, setting up Dicko's fifth goal in three games.
Mali international Sako then calmly beat goalkeeper Tyrell Belford to net the third before Smith turned in Alex Pritchard's cross to pull one back for Swindon after 76 minutes to become the first player to score against Wolves in over 10 hours of football.
Clarke clipped in his first for the club since arriving from Coventry in injury-time to seal the points and please his manager.
Jackett added: "I'm delighted for Leon Clarke to get his first goal for the club having come back from injury.
"He's off the mark and that's good for him and us."