Wharton finished inside the top eight in both races at the Hungaroring, while Sharp recovered from a difficult qualifying session to climb from 19th to eighth in Sunday’s feature race.
The pair initially crossed the line eighth and ninth respectively before two post-race penalties totalling 15 seconds were applied to Theophile Nael, promoting Wharton to seventh and Sharp to eighth in the final classification.
Jose Garfias was also elevated to 11th, completing an encouraging weekend for Prema before the championship’s summer break.
Wharton and Sharp had faced an uphill task after qualifying in 15th and 19th on Friday, despite the Australian finishing just 0.394 seconds away from Tuukka Taponen’s pole time.
The tightly contested session featured 22 drivers separated by less than six tenths of a second, with Prema delaying its first runs in an attempt to find clean air around the narrow and technical circuit.
Wharton was unable to find enough performance to challenge near the front, while Sharp lost his opening run when his car suffered an issue with the power cutting out.
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That left the New Zealander without an early benchmark or an opportunity to make meaningful set-up changes before his final run.
Wharton admitted Prema had work to complete after qualifying but remained hopeful points were achievable despite the Hungaroring’s limited overtaking opportunities.
“Overall a very tough day. We didn’t quite have the pace today as a team and need to now focus on the racing,” Wharton said.
“It’s quite hard to overtake here, but the points aren’t too far away if we have some good races. Overall the pace just wasn’t quite there today.”
Wharton delivered on that prediction during Saturday’s sprint race, gaining seven positions to finish eighth and secure his first points of the weekend.
The opening-lap collision involving Jin Nakamura, Gerrard Xie and Maciej Gladysz triggered a Safety Car, with Wharton having already made immediate progress from 15th amid the early confusion.
He continued moving forward after the restart and reached eighth at the finish, while Sharp advanced seven places from 19th to 12th.
Theophile Nael won the sprint race for Campos Racing after passing Kanato Le for the lead, with the ART Grand Prix driver finishing second ahead of Ernesto Rivera.
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Wharton said returning to the points was an important response after a difficult previous round at Spa-Francorchamps.
“Overall a strong sprint race. It was a good comeback from a tough quali and a tough last weekend,” he said.
“There’s still lots of work to do, but we need to take the positives from today.
“To be back in the points from 15th on the grid, at a track where it’s hard to overtake is a good result.”
Sharp was encouraged by Prema’s race pace but believed his starting position prevented him from converting it into a points finish.
“It was a good race. Pace was really strong, we started 19th and finished 12th so we made up some good positions,” Sharp said.
“I feel like we had the pace to go quite a lot further forward, but it’s hard to overtake around here so we got stuck in the train a little bit, and it was hard to do much more.”
Both drivers continued their progress in Sunday’s feature race, which was repeatedly interrupted by Safety Car and Virtual Safety Car periods.
Wharton and Sharp gained positions during the opening phase before managing their tyres through the second half of the 24-lap contest.
Sharp was particularly aggressive early in the race, completing several overtakes as he charged from the tenth row of the grid into the points.
Wharton finished one place ahead of his teammate to complete his second points finish of the weekend, with the post-race penalties moving the pair into seventh and eighth.
Freddie Slater claimed his first F3 victory after taking the lead when polesitter Taponen pitted with damage, holding off Ugo Ugochukwu to also move into the championship lead.
Brando Badoer completed the podium for Rodin Motorsport.
“Overall I’m quite happy with the race day today, we maximised both races and got points for the first time in both races so have to be happy with that,” Wharton said.
Sharp was equally pleased after recovering 11 positions, although he admitted his early push left him struggling with tyre degradation towards the finish.
“It was a good race going from P19 to P8. I did some really good overtakes. Had a good first few laps and then just picked them off one by one from there,” Sharp said.
“Really happy with the result for the team, it was a good result for all three drivers. I struggled a little bit at the end with the tyres, I felt like I was pushing quite hard at the start, so paid the price for that a little bit later on.
“With how difficult it is to overtake here we had to be on the attack and it’s nice to finish the weekend on a high.”
With two rounds remaining in the season, Wharton sits 15th in the drivers’ standings on 28 points, with Sharp two spots further back in 17th with 21 points. Prema sits seventh in the teams’ standings on 50 points.
F3 will now enter its summer break before a two-day test in Madrid on August 24 and 25, with the championship returning at Monza from September 4-6.
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