It was the Aucklander's third consecutive podium finish at Monaco; having scored two third-placings in the Principality in 2013. His hard-won podium at the third round of the 2014 season lifts Evans from twelfth to seventh in the overall points.
Evans had a better start from the outside of the front row than Palmer and blasted into the lead into the first corner. Behind him, the poleman was busy fending off his teammate Stéphane Richelmi.
Evans started on the super soft prime tyres while his rivals at the front chose the soft compound. The feature race has a mandatory pit stop where each driver has to change to the alternative Pirelli tyre compound.
"I was surprised that the others went on prime at the start because there was a chance of safety car here. I thought that was risky and I was feeling good at the time. The first two laps were good." said Evans. "I was feeling good in the car,"
The Kiwi was on a mission on his super soft tyres and quickly tried to build a gap from Palmer, but his efforts were reduced to nothing after Facu Regalia stopped his car alongside the harbour and the safety car was deployed.
At the re-start, Evans kept the lead and started to push hard again. However, it was not enough. Palmer's blazing pace picked up again and the Briton closed in on Evans to eventually overtake him at Ste Devote.
Richelmi was up next as Evans seemed to be struggling for pace and a small train of cars formed behind the two with Johnny Cecotto also closing in.
Twelve laps into the race mayhem occurred at the tight Mirabeau hairpin after both Arden cars collided with André Negrao sent into a spin and stopping on track. Artem Markelov could not avoid the Brazilian's car and also collided with Negrao, effectively blocking the track as the race leaders arrived.
The race was red flagged. The cars stopped on the grid and after they were all put back into the correct order, the race was re-started under the safety car.
Once the track cleared, Palmer put his head down and set a string of fastest laps to build a gap of nine seconds to Evans who still ran a slower pace than the rivals behind him who were all on soft tyres.
But once again the safety car was deployed. A fight between Julian Leal and Raffaele Marciello for eighth place ended when the Colombian driver tried to pass the Italian before the new chicane and lost control of his car crashing into the wall.
"After the safety car, the prime tyres came into play more and the option dropped a lot and my front tyres started to go away. I just really started to struggle. I was trying to hang in there until our target for the pit stop. We were meant to pit, but the red flag came out so we had to change to the prime tyres on the grid and race it out from there," said Evans.
When all the leaders decided to come in for their mandatory pitstop Stoffel Vandoorne remained in the lead. Palmer re-joined the track behind the Belgian whilst Evans re-joined in fourth place behind Simon Trummer. Both Vandoorne and Trummer still had to change tyres.
With fifteen laps to go, the action resumed. Stefano Coletti wasted no time to put pressure on Sergio Canamasas and passed him at La Rascasse for sixth place. A lap later, the Monegasque driver was all over Felipe Nasr (who had pitted early on lap 7) and also overtook him at the same spot.
He then quickly discarded of Evans before setting his sights on Palmer, but he had one more car in front of him before he could challenge the Briton for the win. Unfortunately for the local driver, as he tried to pass Trummer at La Rascasse, both cars collided ending their race.
Vandoorne finally pitted and Palmer was back in control ahead of Evans and Nasr. In the dying minutes, the Brazilian closed in on the Kiwi but couldn't pass him.
"I was still second and trying to defend my position. I wanted to bring it home from there. I knew I could not get to Jolyon although he was not that quick on the option. Then Stefano passed me in one of the corners we don't really see passing.
"I thought that second place was gone you know. It was a big relief! After that Nasr was behind me with old primes on. I was trying to get to the end.
"Jolyon was struggling on options and there were yellow flags until the end. I think that saved Jolyon a bit. I was a lot stronger towards the end of the race."
Behind the tightly bunched leading trio, Cecotto had to settle for fourth ahead of teammate Canamasas, Arthur Pic (who had started from P14), Rio Haryanto, Richelmi (who will start from pole position on tomorrow's reverse grid), Adrian Quaife-Hobbs and Tio Ellinas.
Evans will start seventh in the Saturday sprint race (02.10 Sunday NZ Time) that has the top eight finishing places in the feature race lined up in reverse order.
