Matias Galarza struck inside the opening two minutes, finding the bottom corner from range to give Paraguay the perfect start at San Francisco Bay Area Stadium.
Turkey dominated possession and created the better chances for long periods, but were unable to find an equaliser even after Paraguay were reduced to 10 men in first-half stoppage time.
Turkey came closest to levelling through Mert Muldur, whose towering header rattled the crossbar and bounced off the upright before the break. Goalkeeper Orlando Gill produced several important saves to keep Paraguay's lead intact as Turkey pressed for an equaliser throughout the second half.
Referee Ivan Barton showed Miguel Almiron a straight red card after the midfielder covered his mouth while exchanging words with Muldur, triggering FIFA's new automatic dismissal rule for the tournament's first time.
Paraguay head coach Gustavo Alfaro praised his players' conviction after the match.
"We were convinced, despite all the adversity, that we could pull it off," Alfaro told Paraguayan broadcaster VS Sports.
Without criticising referee Barton's decisions directly, Alfaro suggested at times it felt as though circumstances were working against his team.
"There were moments when it felt like everything was conspiring against us," the 63-year-old Argentine said. "Sometimes they add time in one direction or another, with excessive added time applied permanently without justification."
It marked Paraguay's third red card in World Cup history, and the seventh dismissal of this tournament, the most at a World Cup since 2014.
Both sides made late changes as the match wore on, with Paraguay introducing fresh legs in defence to protect their slender lead and Turkey throwing on attacking reinforcements at half-time in search of an equaliser that never came.
The result leaves Paraguay third in Group D on three points, back in contention for a place in the next round.
Paraguay face Australia on 25 June for a place in the last 32, while Turkey, already eliminated, take on the United States, who currently lead the group.