Dragons were 14-3 victors when they met at Rodney Parade in the reverse fixture last November, but that was their last win while Connacht's last success was four games ago, against Treviso.
Evans is urging his men to play on the front foot in what are expected to be difficult conditions. And he knows the importance of limiting the ability of Connacht fly-half Dan Parks, who has been named in the hosts' starting XV.
"If Parks is playing, they have got an outstanding ten who can kick them into good positions so we can't afford any indiscipline," the flanker told the South Wales Argus.
"We need to pin them back otherwise it's going to be very tough. Connacht are a bit of a bogey side but the fact of the matter is we need to get a win over there.
"Last season we pushed them very close and, again, should have won but didn't.
"We did come away with a bonus point and if we can go one step better that would be a nice start to 2013.
"Like against the Blues on Boxing Day it can be considered an eight-point game.
"We know how important the game is and need to play like we did against the Ospreys in terms of having a lot of positive moments in the scrums and lineouts.
"Connacht are similar to us in that they're a dogged side with some flair, so we have to fight fire with fire."
Newport have been given a boost with winger Tonderai Chavhanga and centre Adam Hughes returning to their starting line-up. Wayne Evans starts at scrum-half, with Jonathan Evans among the replacements.
Connacht head coach Eric Elwood has made two changes to the team that failed to score in a 17-0 loss at Leinster last time out.
Tongan winger Fetu'u Vainikolo returns from injury and lines up in the back three alongside Robbie Henshaw and Danie Poolman.
The other personnel change sees Mike McCarthy in the second row alongside Michael Swift, while George Naoupu switches to number eight and Eoin McKeon moves to openside flanker.
Most recently Elwood's men suffered back-to-back derby defeats against Munster and Leinster.
And with both sides in the middle of a poor run of from, Elwood believes a win would prove vital.
"This game against Dragons is a vitally important one for the club," he told Belfast Newsletter. "We're side by side at the bottom of the table so this is a huge game for both teams.
"Obviously, with us at home, the pressure is on us to win it.
"The key thing is that we learn from the mistakes of the last two derby matches that we've had. And the main focus for us this weekend is about getting everything right ourselves to secure the win."
At Sportsground, 5pm.
Referee: Andrew MacMenemy (SRU, 18th competition game)
Assistant Referees: Mark Patton, Kevin Beggs (both IRFU)
Citing Commissioner: John Cole (IRFU)