It was driven by two time World Champion Fernando Alonso and his teammate Felipe Massa in his final season at the Scuderia.
In the race, Alonso dropped down the order due to a repeated malfunction of his DRS while Massa picked up two punctures, resulting in finishes of 8th and 15th respectively.
In Spain, both F138s seemed highly competitive during practice sessions but that did not transfer into a much improved single lap pace during qualifying, relative to other teams.
Having passed Räikkönen and Hamilton impressively in the third corner of the first lap, Alonso dominated the race and took his second win of the season while Massa finished in 3rd.
During the weekend in Monaco, once again both Ferraris seemed reasonably competitive during free practice sessions despite Massa's crash into a barrier during FP3 after hitting a bump on the track before the entry into the first corner.
Meanwhile, Massa struggled to fight his way through the rear of the field until crashing into the same barrier as in FP3 due to a damaged suspension, as confirmed by Ferrari.
Despite that, Ferrari remained adamant that this drop in form was an exception due to the Monaco track's unique characteristics.
In Canada, the Ferraris seemed unable to challenge the Red Bull or Mercedes cars for high grid positions in qualifying but, as usual, they recorded decent race pace.
In qualifying, Alonso managed a distant 6th but Massa crashed his F138 on the entry into the third corner in Q2, resulting in a grid position of 16th.
During the race, four cars suffered left rear tyre explosions, one of them being Massa who managed to recover from the back of the field to 6th at the finish.
Alonso, meanwhile, enjoyed a decent race while clearly having a slower car than the two front running teams of Red Bull and Mercedes.
Alonso made a great start and was third behind race leader Sebastian Vettel and second place Nico Rosberg.
As the night race progressed, Alonso made the most of a safety car period and finished in a very creditable 2nd place, albeit 30 seconds behind the winner, Vettel.
Mark Webber's Red Bull expired near the end of the race and Alonso gave the Australian a lift back to the pits, incurring a reprimand for both drivers.