From Caroline Finkel's
Osman's Dream: The History of the Ottoman Empire, usually considered the best narrative history of the Ottoman state (just read the bold part if you're short on time):
Reports from the Ottoman Empire’s northern frontier only served to confirm the threat posed by Peter [the Great of Russia], and in November 1710 the Ottomans declared war on Russia. After a winter spent in making preparations, on 19 July 1711 the advance guards of the two armies, Russia’s led by Tsar Peter himself, confronted one another across the Prut, a tributary of the Danube. That night, Tatar forces swam the river to engage the Russians while Ottoman engineers secured the bridges across the river, allowing the rest of the vastly superior Ottoman army to cross. Peter’s troops retreated a distance from the fighting on the river, but although he found himself surrounded and short of supplies, his men at first resisted the Ottoman onslaught on their positions. On 22 July, after an attack on the Russians by forces led by the grand vezir and commander-in-chief, Baltacı Mehmed Pasha, Peter proposed terms to which Baltacı Mehmed readily agreed. Between Russian prevarication and Ottoman indecision as to whether to continue the war, however, the Treaty of Adrianople, as it is known in the West, was not ratified until 1713; under its terms, Russia lost all it had gained in 1700.
The reason for Baltacı Mehmed’s failure to pursue his undoubted advantage has remained a matter for conjecture, as has the question of whether a more resolute Ottoman stance would have changed the course of history. The argument that the Ottomans lacked either the resources or the will to involve themselves in another and perhaps prolonged war cannot have persuaded the Sultan, who dismissed and imprisoned Baltacı Mehmed. Many years later, in 1763, Frederick the Great asked the consummate Ottoman politician and envoy to Berlin, Ahmed Resmi Efendi, about this battle on the Prut: he was told that the Ottomans’ withdrawal from the fray had been dictated by the Sultan’s magnanimity.
Wikipedia link on the Pruth River Campaign:
Alexander Mikaberidze argues that Baltacı Mehmet Pasha made an important strategic mistake by signing the treaty with relatively easy terms for the Russians. Since Peter himself was commanding the Russian army, and had Baltacı Mehmet Pasha not accepted Peter's peace proposal and pursued to capture him as a prisoner instead, the course of history could have changed. Without Peter, Russia would have hardly become an imperial power, and the future arch-enemy of the Ottoman State in the Balkans, the Black Sea basin and the Caucasus.
Although the news of the victory was first received well in Constantinople, the dissatisfied pro-war party turned general opinion against Baltacı Mehmet Pasha, who was accused of accepting a bribe from Peter the Great. Baltacı Mehmet Pasha was then relieved from his office
So what if Baltacı Mehmed or some other general presses his advantage and captures Peter the Great... in the middle of the Great Northern War?