Tigers trailed 13-8 at half-time and then conceded the opening points after the interval before eventually claiming 34-19 victory and maximum five points.
A place in the last eight of Europe’s premier club knockout competition was confirmed by results elsewhere on Saturday evening and Tigers director of rugby Cockerill said: “Treviso came out of the blocks very well and we were inaccurate in the first half.
“Credit to Treviso because they were very good, and credit to Leicester for keeping our composure. When we got our rhythm we took our opportunities and got the bonus point which was crucial for us.
“They put us under a lot of pressure but our players reacted and rallied very well, and didn’t let things get on top of us. In the end we played some good rugby and scored four tries.
“Nobody has had it easy here – they make it very difficult for you, they are big and physical, and a difficult side to play against.
“Ulster got a bonus point in the 78th minute here, we got a bonus point in the 79th minute at home against Treviso. They have a lot of Test players, they always make it hard for you and that makes composure very important.”
Cockerill welcomed back Anthony Allen, Steve Mafi and Rob Hawkins to the matchday squad after lengthy absences and all made a contribution as the momentum swung in Tigers’ favour in the second half at the Stadio Monigo.
“It’s great to get guys back in the mix and they all made an impact,” said Cockerill. “There are lots of positives there with the games we have to come in the second half of the season.”
Tigers host Ulster on Saturday (6pm) in the last game of the pool stages, with top spot in Pool 5 and a home draw in the quarter-finals at stake.