A bruised and bloodied Lee Cowmeadow led the charge as Swindon finally broke their home drought - but they made hard work of their first home win of the season with another dreadful start.
Wildcats went a goal down after only 20 seconds as Rastislav Palov received a good pass all alone on the edge of the blue line, before taking the puck past Nathan Craze in the Swindon goal.
On the five-minute mark, with two Cats players sitting minor hooking penalties, Chieftains made it two - Scott McKenzie converting a slick passing move without too many challenges.
It was familiar territory at 8.48 when Palov scored his second, and for the third time this season Swindon trailed 3-0 on home ice.
Coach Peter Russell immediately called a rare first period time out to attempt to pull his team together.
Cowmeadow, who has enjoyed success at Cardiff and Slough during his long career, finally ended a spell of sustained offence with the Cats first goal. He slotted the puck home at 12.20 after good work from Adam Brittle and Tomas Janak - who had threaded through a fine long pass.
Brittle and Janak combined again for Matty Davies to score at 17.51 so that Cats trailed 3-2 at the first break. After nearly nine minutes of another disjointed home display, the signs were at long last improving.
The second period proved to be the best 20 minutes of play for the Cats at the Link Centre this season.
Eric Bochna, showing his best home form so far, levelled the scoreline at 24.26. With their lead gone, Chelmsford then began to incur penalties from referee Rene Ross, who generally had a poor game.
The go-ahead goal came from the out-of-form Marek Hornak at 25.48, with fellow Slovakian Bochna's check on the boards a sturdy one which then allowed him to feed the puck through.
Cowmeadow scored his second and the Cats fifth at 38.12, again on the power play. But as he netted the Cats' assistant captain took a stick to the head which left him visibly hurt.
Blood on the ice had to be cleared before the game could re-start, but bravely he appeared for one final shift before the second period ending with Swindon holding a 5-3 lead.
There was another twist in the tale - in fact a double - as the visitors twice netted short handed though Palov for his hat-trick at 44.03 and Mattila at 47.57 to level the scores at 5-5 Then, just as talk began of a possible five-minute overtime, the Cats scored their match-winner.
In the Cats' best offensive move of the game, Cowmeadow and Bochna prised open the Chelmsford goal and Lee Richardson pounced to score the game-winning goal at 54.49.
In the closing stages any Chelmsford threats were killed off as they took a host of penalties leaving them only three outfield skaters.
The fans and coach Russell were put through the mill in this clash, but it was excellent end-to-end entertainment - and at last a first home win to go alongside two victories on the road.
Hero Cowmeadow had to change his shirt from his normal five to 20 for the final period, but again he showed good work rate and leadership.
He admitted: "I took a stick in the head, and I'm going to have the cut looked at. Overall though it is just a relief for the boys and the fans to finally put a home win on the board.
"We all know it is well overdue but I think the team can be given credit to put in such a big effort after going three goals down. I can only say that in the end we did show real pride, and we started to do the coach's training drills more and more."
Russell praised the efforts of his British players. "I thought the British lads played really well tonight," he said.
"This is a good team but to get up to where we expect to be after disappointments this is one step along the way.
"It was a bad, flat start again, but we proved that we have grit and determination. It showed that we could grind out a result and we needed to show that.
"It takes time for things to come together.
"It's time to look at juggling things around, especially on the powerplays where we conceded two shorthanded goals.
"Then if some areas don't improve radically we would have to reluctantly consider making a change."
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