Team-mate Sebastian Vettel also benefitted from a strategic masterstroke to finish fifth and pick up his first points for the Silverstone-based team.
After a difficult start to the season with both drivers struggling to get to grips with the AMR21, Stroll praised the team for its efforts in Monaco.
"Yeah, it is always tough mentally, it is very demanding, you have to stay focused from lap one until the end," said Stroll.
"Around here, with the walls, there is no margin for error and it is always very intense. Happy with the job and good to pick up some points.
"It was a good day for us. We had a good strategy, had some good pace on the first stint, when the others pitted on the soft tyres we were on the hard and went very long and had some good pace at the end of that hard stint.
"We were able to overcut Ocon and Giovinazzi so a great day for the team with both cars in the points."
Talking of his prospects in Baku next time out, Stroll added: "I think we are learning every race so definitely some things to take away from this weekend and we will come back stronger in a couple of weeks."
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