The Tuscan club had started the day at the foot of the Serie A table, but Innocent Emeghara's brace and a further strike from Alessandro Rosina capped a superb performance against a Lazio team challenging for a Champions League place.
The win saw Siena move to within four points of safety and Iachini admits it was a result to savour.
"The guys gave a great performance, you have to play well to beat Lazio," he said on acsiena.it.
"We played the game in the right way and are reaping the rewards of the great work we do during the week.
"We had prepared well for the match. We were careful in attack and then good hitting on the break."
Iachini is hoping his players can now go on a winning run as they look to climb out of the bottom three.
"The secret to this success is organisation, intensity and the right mindset to always go looking for a victory by playing proactively," he said.
"We have to continue like this, always believing in the work we do.
"I do not look at our ranking now, it makes no sense to do so. We will just try to win as many games as possible, then we will do the maths at the end."
Lazio remain third in the table but are 11 points behind leaders Juventus and without a win in their last five league matches.
Coach Vladimir Petkovic admitted his side were outplayed by Siena.
He said: "I take the blame for the team and the tactics, but you have to compliment Siena for the way they played. There are no excuses for this defeat.
"I did not need to shout at the players - they are smart and know what they did wrong.
"We also have to apologise to the fans because they did not see the real Lazio."