During the 2013 Monaco Grand Prix weekend it was announced Toro Rosso had signed a long-term agreement with Renault to use their engines from 2014. On 21 October 2013, it was announced that Jean-Éric Vergne would remain with the team for a third successive season, and will be partnered by Daniil Kvyat, who was a race-winner in the GP3 Series and the FIA European Formula 3 Championship in 2013.
The team made an impressive start at the Australian Grand Prix with Vergne qualifying 6th, Toro Rosso's best qualifying result since the 2013 British Grand Prix and Kvyat qualifying 8th. The drivers finished the race 8th and 9th respectfully to score Toro Rosso's first points of the season, as a result of this Kvyat had broken Sebastian Vettel's record as the youngest points scorer in Formula One history. At the Malaysian Grand Prix Vergne qualified 9th while Kvyat qualified 11th, the race was going well for them until on lap 18 Vergne suffered a power unit failure in his car which has been a common occurrence in Renault powered cars so far this season meanwhile Kvyat finished 10th and scored 1 point but was ultimately a lap down from the race winner.
At the Bahrain Grand Prix, both Vergne and Kvyat qualified well down the field in 13th and 14th; Kvyat finished 11th while Vergne retired due to a collision, while at the next race in China, Vergne qualified 9th and Kvyat 13th, but Kvyat was able to score a point in 10th place. At the Spanish Grand Prix, Kvyat once again qualified 13th while Vergne started 16th. Kvyat finished 14th, a lap down from the race winner while Vergne retired from the race due to an exhaust problem. At the Monaco Grand Prix, both cars qualified in the top ten, as Vergne was seventh while Kvyat qualified in ninth. Both drivers were unable to finish the race however, with exhaust issues causing each retirement. At the Canadian Grand Prix, Vergne started 8th while Kvyat qualified in 15th; Vergne finished where he started, while Kvyat retired due to a driveshaft failure.
At the Austrian Grand Prix, Kvyat took his best qualifying position with 7th, while Vergne lined up from 15th position. The team suffered another double retirement, as Vergne retired due to an issue with his brakes, while Kvyat was sidelined with a suspension problem. At the British Grand Prix, both cars once again qualified in the top ten with Kvyat ninth and Vergne tenth. For the first time since Australia, both drivers scored points, as both Kvyat and Vergne finished where they started, in ninth and tenth places respectively. At the German Grand Prix, Kvyat qualified eighth, five places ahead of his team-mate. Vergne finished the race in 13th, while Kvyat retired from the race, after his car caught fire. In August the team announced Kvyat and Max Verstappen as their drivers for the 2015 season. However, on 3 October 2014, Red Bull Racing announced Sebastian Vettel's departure from the team, and stated that Kvyat would be promoted from Toro Rosso to pair with Daniel Ricciardo. Among the candidates being considered for the second seat were Vergne, as well as Red Bull Junior Team drivers Carlos Sainz, Jr. and Pierre Gasly – who finished first and second in the Formula Renault 3.5 Series – and Alex Lynn, the GP3 Series champion. On November 26, 2014, Vergne announced he would be leaving Toro Rosso. Two days later, Toro Rosso confirmed that Sainz would partner Verstappen for the 2015 season.