Eric Elwood's men have collected three losing bonus points in their last three games, with defeats to Benetton Treviso away (24-17), the Ospreys at home (16-15) and Edinburgh away (24-19).
Two unconverted tries from winger Brian Tuohy, in the opening quarter, saw Connacht set out their stall at Murrayfield.
And although Edinburgh got back on terms for half-time (10-10) and then pushed on with full-back Chris Paterson tallying up 16 points, the visitors managed to garner a losing bonus point thanks to three penalties from out-half Miah Nikora and replacement centre Ian Keatley (2).
A second successive win on Scottish soil was not to be, but Connacht had at least managed to banish memories of their 32-5 and 62-13 losses to Edinburgh at the home of Scottish rugby in the past two seasons.
"We're disappointed we didn't win the game (against Edinburgh), we had a great start scoring two tries and going 10-0 up, and even in the last few minutes of the game we had opportunities to finish it out - but we'll take the positives out of the game," admitted Elwood.
"The last couple of times we've gone to Murrayfield we've taken a bit of a hiding, so this really shows how far we've come.
"The guys have really stepped up to the mark - Brian Tuohy, Eoin Griffin, Dermot Murphy - these guys are doing the business and putting their hand up for selection and it's great to see it."
It is this encouraging strength in depth which is keeping Connacht competitive in both the Magners League and Amlin Challenge Cup this term, and a victory on Friday could see them gain a place or two in the league table.
"To come back from being 21-10 down shows a lot of character from the boys, to come back into bonus point territory allows you to press ahead and go for the win and maybe with a small bit more composure we could have closed out the game," reflected the former Connacht and Ireland out-half.
"We're trying to play a bit more expansively and increase the interplay between the forwards and backs and I think we really showed that against Edinburgh last Friday.
"There were some great standout performances in that game, Brian Tuohy really made his mark with two well-taken tries, Dylan Rogers came on and had a great game.
"Ian Keatley did well and gives us a few options in the centre now and Johnny O'Connor had a fantastic game.
"We're looking forward to taking the momentum from last Friday's game into this week's clash with Aironi. They've struggled to get results in this campaign and will look to the game against us as a means to get their season back on track.
"So we're expecting a battle alright, they were 10-0 up after 30 minutes at home to the Scarlets last week so we know they can score points, but we're confident in our own ability, confident in our own defence and we'll stick to our gameplan and back ourselves."
The Connacht management have a number of injury concerns ahead of Friday's meeting with the Italians. Young centre Eoin Griffin has broken a finger and is expected to be out for four to six weeks, while Samoan duo Niva Ta'auso (cheek) and Ray Ofisa (eye socket) remain on the injury list.
Hooker Adrian Flavin (thumb) and top try scorer Fionn Carr (leg) are receiving treatment, with Elwood hopeful that Carr will be fit to play this weekend.
Also trying to overcome knocks are Keatley (calf), Keith Matthews (back), Darragh Fanning (hamstring), Shane Monahan (ankle) and Ezra Taylor (calf).
"This will be Aironi's first visit to the Sportsground so we hope there'll be a big crowd out to welcome them and cheer on Connacht.
"Having a large home crowd makes a big difference to the lads on the pitch, it gives them an extra boost so hopefully we'll see a large turnout on Friday night."
To coincide with the end of Movember, Connacht are running 'the Italian Job' ticket sale. Between the hours of 1pm and 5pm today, all tickets for the Connacht v Aironi match are on sale for only €10.
This offer is available through Ticketmaster or by calling in to the Connacht Rugby office in the Sportsground. It is a limited offer available only during the stated times, so fans are advised to act fast to secure their €10 ticket.