Initially they tore up the form book and went about taking control of the tie, eventually running in six tries to win 44-31 at Stadio Monigo.
However, that wasn't before a nerve-wracking Treviso comeback late in the second half, which had Easterby and his team fearing a repeat of last season's meeting.
"We always make it interesting when we come here," he said. "Last year we got ourselves into a good position and lost the game.
"Today we held on and took the win. We scored some good tries and came away with a bonus point win. The disappointing thing is we probably lost control again for a little while in the second half and gave them an opportunity to pressurise us.
"Coming here hasn't always beena happy hunting ground for us but we came here today, created lots of good opportunities and got what we deserved.
"Any win away from home is good. We have a lot of players absent at the moment but the guys really stood up here today.
"They played well and that's all we can ask of these guys at the moment is to keep climbing the table, keep putting the pressure on sides around us and try and move upwards."