The win was Milan's second in two league matches under Rueben Amorim and ended a frustrating run of four Serie A home games without a victory. Venezia, meanwhile, remain without a point following their return to the top flight.
There were emotional tributes before kick-off to Milan legend Franco Baresi, and the Rossoneri produced a strong defensive display, although they initially struggled to turn their attacking pressure into goals.
Ramos could have opened the scoring after 12 minutes when Samuel Chukwueze played him through on goal. The assistant referee kept his flag down, but Venezia goalkeeper Filip Stankovic made an excellent save with his right hand.
Venezia responded with a dangerous attack of their own when John Yeboah sent Akor Adams through. Chukwueze tracked back well to force Adams wide, allowing Mike Maignan to make a comfortable save.
The visitors grew in confidence and caused problems inside the Milan penalty area following a Ridgeciano Haps cross. The ball eventually fell to Yeboah, but Strahinja Pavlovic produced an important block.
Milan soon regained control and Ramos was again denied by Stankovic, who saved his first-time effort from close range. The Portuguese forward continued to find opportunities, while Koni De Winter and Chukwueze also went close before half-time.
Venezia remained competitive after the break and Antoine Hainaut fired across the face of goal. Milan then wasted a huge opportunity when Yunus Musah struck the crossbar from close range following a Luka Modric free-kick.
The visitors continued to threaten, with Adams finding space inside the penalty area, but Mario Gila made a crucial block to keep the score level.
That intervention proved decisive.
Just two minutes later, Milan finally found their breakthrough. Alexis Saelemaekers drove forward down the left before cutting inside and slipping a pass through to Ramos, who calmly fired a low shot into the bottom corner.
It was Ramos' first goal for the Rossoneri and gave Milan the breathing space they had been searching for.
Amorim's side then controlled the closing stages and secured the victory with a second goal. Ardon Jashari was played through on goal and saw his effort saved by Stankovic, but the rebound struck the retreating Redouane Halhal and rolled into the net for an own goal.
The 2-0 result continues Milan's strong start under Amorim, while Venezia's difficult return to Serie A goes on. The promoted side are still searching for their first point of the campaign and are now without a victory in 27 away matches in the Italian top flight.
