Aironi (10) 17
Tries: Tebaldi, Pizarro Con: Tebaldi 2 Pens: Tebaldi
Scarlets (13) 34
Tries: Stoddart 2 J Edwards, Maule Con: Preistland Pens: Priestland 3 Drop: Priestland
Morgan Stoddart crossed the Aironi try-line twice for the Scarlets
Scarlets climbed up to second in the Magners League with a bonus-point win over bottom side Aironi.
They had to wait until the last 11 minutes through to run home three of their four tries.
Morgan Stoddart claimed two of them, while there was one each for Jonathan Edwards and Gareth Maule.
Tito Tebaldi scored 12 of Aironi's points including one try, while Gabriel Pizarro grabbed the other for the winless Italian side.
Aironi had led 10-0 before the Scarlets came back, Stoddart's first score helping them to a 13-10 half-time lead.
It remained in the balance as Pizarro put the hosts back in front but Nigel Davies' side held their nerve and pulled clear in the closing stages, with Stoddart rounding off the win.
Tebaldi kicked the hosts in front from an early penalty but missed three more before the scrum-half's try and subsequent conversion put his side 10 points up after 27 minutes.
Scarlets fly-half Rhys Priestland had also missed the target with a ninth-minute place-kick but was successful four minutes after Tebaldi's try to cut the deficit.
And winger Stoddart touched down four minutes before half-time, Priestland converting and adding a drop goal in the last minute of the first half to send his side into the interval 13-10 to the good.
Another Priestland penalty stretched the margin to six points - but that was wiped out as centre Pizarro went over in the 56th minute and Tebaldi converted to put Aironi 17-16 up.
The Welsh side's response was almost immediate as Priestland added another three points on the hour mark.
That settled their nerves and three tries in the final 11 minutes ensured they would complete an ultimately comfortable win.
Flanker Edwards and centre Maule both crossed before Stoddart added his second a minute from time, Priestland missing all three conversions to complete a mixed day for kickers.
Scarlets Head Coach Nigel Davies said: "This was an important win for us and it was pleasing for us to achieve a bonus-point victory away from home in terms of our Magners League campaign and it could be significant for us later on.
"It's encouraging that the belief building in this team meant that the boys remained calm, focused and didn't panic when the score-line was tight - we were under pressure for large parts of the game but when our opportunities came, we took them very well.
"Three of the four tries were from set-piece moves and it was good to see that happening at a crucial time in the game when we needed to close it out."
Aironi Rugby: Laharrague, Toniolatti, Penney, Pizarro, Pratichetti, Marshall, Tebaldi, Aguero, Santamaria, Staibano, Bortolami, Furno, Sole, Krause, Williams.
Replacements: Redolfini for Staibano (48), Favaro for Krause (54).
Not Used: Ferraro, Milani, Biagi, Wilson, Buso, Rubini.
Scarlets: Evans, Stoddart, Maule, King, Reynolds, Priestland, Knoyle, I. Thomas, Owens, P. Edwards, Reed, Day, Morgan, J. Edwards, Lyons.
Replacements: John for P. Edwards (45), Welch for Reed (41).
Not Used: Phillips, Gardner, Fa'amatuainu, Roberts, Newton, S. Williams.
Ref: Andy MacPherson (SRFU).