The second half brought a second try for Aironi, through powerful back rower Nick Williams, but by then veteran Chris Paterson had already added a fourth for Edinburgh to make sure of the bonus point.
Looking to string together two consecutive home wins for the first time since November, Edinburgh made the best possible start with seven points on the board inside four minutes.
McKenzie, whose move to Sale next season was confirmed this week, finished a move that had swept across the pitch and back again after a precise lineout feed by Scott MacLeod.
Greig Laidlaw converted and put his side 10-0 ahead with a penalty from distance in the 13th minute after he had been blocked following his own chip ahead.
However, Laidlaw turned sinner four minutes later as the Italians built their first meaningful attack. He deliberately knocked on a pass from Matteo Pratichetti that threatened to put Williams over. James Marshall landed the resulting penalty.
Referee John Lacey had sent Laidlaw to the sin-bin, so when a penalty came Edinburgh's way three minutes later full-back Jim Thompson was called upon but failed.
Lacey had his yellow card out again in the 27th minute, sending both Edinburgh lock Esteban Lozada and Aironi's Marco Bortolami to the sin-bin after their involvement in an off-the-ball incident.
When play resumed, Edinburgh swiftly forged ahead with tries after 30 and 34 minutes. Firstly, scrum half Blair broke clear from a ruck to score and then Visser raced past two defenders to claim his 13th try in 19 Magners League games this season.
The Dutch winger's effort gave him a new record for the most tries by a player in a league campaign, eclipsing the previous best of 12 set by Jamie Robinson (Cardiff Blues) and Kevin Morgan (Newport Gwent Dragons) in previous years.
Laidlaw topped off both tries with conversions, however, right on the stroke of half-time, Aironi scored a try through Demas, who was sent in from a slick pass by Gareth Krause.
Marshall missed the conversion, leaving the half-time deficit for Rowland Phillips' side at 24-8.
Aironi had the better of the territory in the early stages of the second half, coming close to a second touchdown when the ball was briefly lost in a forward pile-up on the home line.
They came even closer in the 58th minute, with only a cracking tackle by Visser stopping Demas from scoring.
A minute later, in cruel fashion for the Italians, Edinburgh scored their bonus point try. Off an interception, replacement Nick de Luca ran half the length of the pitch before allowing fellow replacement Paterson to hare in.
The busy Italians were not deterred and hit back with their second try, number 8 Williams breaking through with Marshall adding the extras.
As the game ran its course, Laidlaw knocked over a penalty to confirm a victory that takes Edinburgh up one place in the league table to eighth.
Praising number 8 and man-of-the-match David Denton and his team's overall effort, Edinburgh's interim head coach Nick Scrivener said: "I thought David had an excellent game, both in terms of the directness he brought to our play and his energy across the match.
"He's still very much a work in progress, but there's a lot there for us and him to get going with, and if he keeps showing the same desire and application, he's going to be a big player for this club.
"I'm more than happy with our work all-round, because even though Aironi made life difficult for us at times at the breakdown, we showed a clinical edge in attack and made sure they didn't get close to us on the scoreboard at the start of the second half when they had a fair bit of possession and territory.
"I'm delighted for Tim (Visser) that he got on the scoresheet again - his finishing ability is first class and it's great to be able to call on that.
"He's another one who keeps working hard at his game, and I'm convinced he'll keep getting better and better."
|Edinburgh Rugby Score Card|
|Aironi Rugby Score Card|