Riccardo Bocchino knocked over a third penalty for the Italians and they looked set to claim a famous victory until Scotland cap Jacobsen barrelled over with four minutes remaining, Blair adding the critical conversion.
Blair had slotted the first points of the evening after his up and under had caused panic in the Aironi ranks, nailing a fourth-minute penalty.
But former Gloucester stand-off Mercier quickly levelled the scores after the Gunners were penalised for collapsing a scrum in front of their posts.
Aironi's physical defence at the breakdown was causing the visitors real problems, and a string of handling errors stymied their attacking efforts with flanker Alan MacDonald and wing Mark Robertson failing to hold onto the ball after some purposeful carries from the pack had put Edinburgh in promising positions.
Mercier was then off target with a drop goal and a penalty, but made amends as he kicked his second penalty on the stroke of the interval to give Aironi the lead.
Jacobsen came off the bench and won a penalty at the scrum for his side, but Blair's long-range effort came up short.
Bocchino, on for Mercier, was also off target with a penalty but the home side's hopes were boosted as MacDonald was sent to the sin-bin as the penalty count mounted against Rob Moffat's men.
Aironi had a series of drives close to the visiting line but 14 man Edinburgh did well to hold them out, although Bocchino did increase Aironi's lead with a penalty with 10 minutes remaining.
But the Gunners hit back with a powerful maul forcing Aironi lock Carlo Antonio del Fava to concede a penalty, the Italy international receiving a yellow card for his troubles.
The visitors again opted to go for a driving line-out and this time it paid off as Jacobsen crashed over and Blair added the extras to spare Edinburgh blushes.
|Aironi Rugby Score Card|
|Edinburgh Rugby Score Card|