After taking an emotional pole on Saturday, Sainz produced a combative display at Monza in front of Ferrari's tifosi, putting on a strong defence in the first stint of a one-stopper in an attempt to keep Verstappen's quicker Red Bull at bay.
Sainz used his Ferrari's excellent top speed to successfully defend his position several times into the first two chicanes. But following a lock-up into Turn 1 on lap 15 the Spaniard had to allow Verstappen through into Turn 4, and soon had to focus on safeguarding second place against Verstappen's team-mate Sergio Perez.
Sainz, who after the race was robbed outside of his Milan hotel, ultimately settled for third behind the two Red Bulls, beating team-mate Charles Leclerc to the coveted final podium spot, as Ferrari allowed the pair to continue their spirited battle to the finish.
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But afterwards he revealed there was a brief moment in the first stint when he believed he could pull off a shock win in front of the adoring Italian home crowd, until he realised he had pushed his tyres too far in an attempt to keep Verstappen behind.
"Yeah, halfway through it," he said. "I felt like I had [it] fairly under control but then around lap 10 to 12 I started feeling the rear left tyre giving up a lot, a lot earlier than I would have expected.
"At that point, I realised I had used my tyres too much, probably to keep Max behind.
Source: Autosport