Kurzawa opened the scoring from close range in the 36th minute and Ocampos sealed the victory with a splendid overhead kick two minutes from time as Monaco moved up to 45 points from 21 games.
Champions Paris St Germain can re-establish their five-point advantage if they beat sixth place Nantes at home later on Sunday (2000 GMT).
"We have not played well after the winter break so I'm very happy with this victory. I hope that we're back on track," Monaco coach Claudio Ranieri told broadcaster beIN Sport.
Monaco were second best throughout the first half but took the lead with their first chance when Kurzawa found the net from Geoffrey Kondogbia's low cross.
The 21-year-old full back, playing his first season in the top-flight, has now scored in three consecutive away league games.
Monaco upped the pace after the break and striker Radamel Falcao came close to scoring his first goal in two months when he skipped past goalkeeper Ali Ahamada, only to see midfielder Abel Aguilar clear his attempt on the goalline.
The 19-year-old Ocampos, who had replaced Colombia international Falcao in the 68th minute, eventually wrapped it up with a superb finish from James Rodriguez's long cross.
- Sports & Recreation