The 30-20 home loss to Northampton Saints in the LV= Cup on Sunday made it seven defeats in a row in all competitions for the Dragons, their worst run since the region was formed in 2003.
Lewis Evans and prop Phil Price return to the starting XV at Rodney Parade, while Jack Dixon and Ieuan Jones retain their places on the bench after impressing against the Saints.
Ashley Smith is also available despite going off with a suspected broken hand on Sunday, with a medical scan showing no serious damage.
And while there may have been positives in the performance against the Saints, Brown admitted he was still left red-faced.
"I was gutted to hear that we had set a record," he said.
"It made me think back to games that we should have won, all we needed was one moment of brilliance but we came up short.
"We need to end this run and even though it was another loss against Northampton, we were a lot sharper.
"But I have never been one to let my shoulders slump and I hope nobody else does, because you're never going to have things all your own way in a game.
"It will be an all guns blazing game and Connacht will be targeting us just as much as we are targeting them.
"They are abrasive, horrible at the breakdown and big, physical men while Dan Parks has the ability to control the game from fly-half.
"Connacht will be hungry to beat us but we really need this. One win could easily turn our season round and give us a real boost.
"I'd take a 3-0 - winning ugly is much better than losing pretty."
Connacht have not played since beating Treviso 18-3 on November 3 and make three changes with Gavin Duffy returning to the starting line-up to skipper the side on the wing.
Duffy came off the bench for the last seven minutes against Treviso after several weeks out with injury and went over soon after his introduction.
Danie Poolman makes his third outing for Connacht with Dave McSharry joining him in the centre and Tiernan O'Halloran at right wing.
With Mike McCarthy still on international duty this week, Mick Kearney comes into the second row alongside Michael Swift.
After returning to training this week, hooker Ethienne Reynecke is among the front row replacements alongside winger Matt Healy who could earn his first cap for the province.
Connacht are looking for back-to-back RaboDirect PRO12 victories for the first time since April thoughthey have only three wins on their travels in all competitions in 2012.
Scrum-half Kieran Marmion has given Connacht a boost ahead of the clash after signing a new contract to keep him at the province until 2015.
The 20-year-old has represented Ireland at U-18, U-19 and U-20 level and starred at last summer's Junior World Cup and starts at No.9 against the Dragons.
Marmion made his debut for the Westerners this season against Cardiff Blues in their RaboDirect PRO12 opener, and cannot wait to add to his ten appearances.
"It was a great experience to go over to South Africa and play against the best U20 players in the world," said Marmion.
"To start for Connacht this season was fantastic. I'm thrilled to have extended my contract with the province.
"I feel at home here and I want to continue contributing to the squad and the great work that is being done here every week."
At Rodney Parade, 7pm.
Referee: Giuseppe Vivarini (FIR, 4th competition game)
Assistant Referees: James Jones, Kevin Shorte (both WRU)
Citing Commissioner: Ray Walton (WRU)