Speaking for the ancient Greeks: almost certainly yes, but it never settled anything, so they stopped doing it.

It happened once during the three kingdoms.

On the 22nd of May 192 the tyrannical controller of the Han Dong Zhuo, having survived a few plots, was killed by his bodyguard Lu Bu and his chief minister Wang Yun and they quickly destroyed Dong Zhuo's family at the capital and his stronghold at Mei. However some of Dong Zhuo's officers had been away raiding during this and returned home to an uncertain situation, they sought an amnesty as an assurance of safety but Wang Yun refused. His execution of the famed scholar Cai Yong and high-handed manner alienated people and there were rumours that Wang Yun was going to kill figures from Liang province like Dong Zhuo's returning generals, further spreading concerns. So, on the advice of Jia Xu, they allied with each other (Li Jue treated as the senior general) and marched on the capital Chang'an with the Han armies deserting or being defeated.

When Li Jue and party reached the capital, according to contemporary Wang Can who was at the capital at the time, there would be a duel between senior general Guo Si and the Han commander Lu Bu, a man famed for his abilities as a warrior. Lu Bu's SGZ, translation Yang Zhengyuan

​

Guō Sì was north of the city. (Lu) Bù opened the city gates, led troops to face [Guō] Sì, and said: “Let us both withdraw troops, and ourselves personally decide victory.” [Guō] Sì and Bù then dueled, and Bù with a spear stabbed [Guō] Sì. Riders behind [Guō] Sì then came forward to rescue [Guō] Sì. [Guō] Sì and Bù then each withdrew.

Did it help the new Han regime to see their commander's display of warrior skill? No. Guo Si recovered Within eight-ten days of besieging the city, less than sixty days from Dong Zhuo's assassination, there was a mutiny from members of Lu Bu's army and on the 28th June, the gates were opened. Lu Bu attempted to resist but the cause was lost, Lu Bu fled with some horsemen while Wang Yun refused to go, prepared to face his death. He would be seized and once the new military junta's position was secured, executed on the 4th July.

While there would be a few (but only a few) other duels between the collapse of the Han in 190 and unification in 284, most famously the scout Taishi Ci with the warlord Sun Ce, they would be as officers coming across each other rather than such a formal everyone standing aside. Like the Lu Bu vs Guo Si duel, the duels could be inclusive and it didn't change the wars they were fighting in. The battles and the wars continued, the only one that might gain is the warrior via reputation and even here, Lu Bu is more remembered for his archery to stop a war than for this duel.

The era is famed for its duels but that is due to the novel Romance of the Three Kingdoms which changed the way the war was fought among many other changes. In the romance, there were many many duels and many many kills (the elderly Shu officer Zhao Yun killing a fictional father and seven sons during one campaign for example) including some big set-play duels to excite the audience like the coalition vs Dong Zhuo, Hua Xiong's rampage then his off-screen end or Lu Bu's rampage before facing the three brothers (Liu Bei, Guan Yu, Zhang Fei) rather then the historical war of blockade and Sun Jian's victories. Or for the famed warrior to kill rival champion quickly in a show of their great skill which leads to victory as the losing side collapses upon that defeat as the victorious side charges at them.

The Lu Bu vs Guo Si duel is not included in the novel.