Wall of text warning...
What people consistently fail to consider is that no Spitfire ever encountered the Zeke in 1941... Nor in 1942... The first combat Spits didn't arrive in the Far East until 1943, and then they were still only Spit VC Trop of 1941 origin. In the air battles over Darwin where these 1941 Spit V's met the Zeke for the first time they faced not the 1941 model A6M2, but the late 1942/early 1943 A6M3. These Zekes were much more comparable in performance to
the now two year old Spitfires, especially since the Spits were tropicalized with the cumbersome and much maligned Vokes air filter which reduced the already outdated Spit V's performance. By 1943 the Allies had long since discovered the Zeke's performance advantages and flaws so there were no surprises left in them.
The first battles between the Spitfire and Zeke came about as a result of the Australian city of Darwin being bombed repeatedly in 1942. In response Churchill dispatched a wing of Spit VCT's to defend the city. The squadrons became known as the "Churchill Wing", although they were almost entirely crewed by Australians. The first Spits became operational in early February 1943.
On February 6, 1943 they drew first blood, shooting down a Ki-46 Dinah recce bomber, but it was to be the 2nd of March that they first faced Zekes: 21 A6M3s of the 202nd Kokutai escorted 9 G4M Bettys of the 753rd on a raid against Darwin. 20 miles off the coast a flight of six 54 squadron Spit Vs caught the raiders. An 8 minute dogfight ensued and both sides claimed to have shot down several enemies, but in fact only one Spitfire and two Zekes were damaged. Wg Cdr Caldwell noted that in tight 160 mph turns the Zeke didn't get dangerously close until after the second turn. He "easily evaded the Zeke with a downward break".
On March 15, returning from night ops and with their oxygen supply depleted, 452 sqn attacked a force of 50 Japanese aircraft split evenly between fighters and bombers. Four Spitfires were lost, but four Zekes were shot down along with three bombers, and a further seven Japanese aircraft were damaged. Two of the Spitfire pilots downed were killed, including the 452's CO, Sqn Ldr Thorold-Smith.
On May 2nd another 50 plane Japanese raid was met by all 33 of the Wings operational fighters. In a twenty five minute running battle the Spitfires suffered five losses, but claimed ten enemy aircraft in return with many more damaged. However, a further ten Spitfires were lost to fuel shortages and technical problems... The press release from MacArthur's office stated they had suffered a "severe reverse". With no way of knowing how many of their damaged foes made it back to base there was no way to refute the report; the mud stuck. When the air war over Darwin is mentioned today, the loss of 15 Spitfires for just 10 enemy aircraft inevitably surfaces. Usually with a snide comment about the accuracy of the 10 claimed by the Aussies...
On May 9, Spitfires destroyed two Zekes and damaged a third. One Spitfire was lost in a landing accident.
May 28, six Spits met thirteen Japanese aircraft. They lost two of their own, but shot down two bombers and damaged a third.
On June 20 the JAAF decided to try their luck. 30 bombers and 22 Ki-43 Oscars were met by 46 Spit VCT's. 9 bombers were destroyed, 8 more damaged, 5 Oscars were shot down and 2 damaged without losing a single Spitfire.
On June 28 a mixed bag of 18 Zekes and Bettys were bounced by 457 sqn. 3 Zekes were destroyed, 2 bombers probably joined them, for no RAAF losses.
June 30 saw the Japanese attack the USAAF base at Fenton with 27 Bettys and 20 Zekes. 4 bombers were destroyed, 4 more probably destroyed, 3 Zekes were destroyed with 6 probables, for no Spitfires lost.
July 6 saw 26 bombers and 21 fighters being engaged by the Spits. 9 Japanese aircraft were destroyed. 2 Spitfires were shot down, but 6 more were lost to mechanical failures.
The Japanese had finally had enough; they switched to night bombing...
The Spitfires, on the other side of the world from their supporting factories, often heavily outnumbered and suffering from conditions that their desert fighters were never designed to cope with, had achieved the task Churchill set for them. Far from being defeated by the Zekes, they ground them down until they could no longer support further attacks. Skill, courage and a superb fighter carried the day, even if the Spits were two years out of date, and was up against the elite 202nd Kokutai. The Japanese lost 60+ aircraft over Darwin. They shot down 16 Spitfire V's in return.

Btw. I ripsnorted a lot of the engagement figures, so don't quote me as an original author.