And there are quite a few other episodes where Kirk won because he got lucky. The kind of luck that can make one win the lottery.
Archer was written as depending far less on luck than Kirk.
There were planty of episodes where every captain got 'lucky' and were saved at the last minute with some technobabble thing. Episodes where the Q or Guinan help Picard, where 'The Prophets' give Sisko advice, where the Borg let Janeway go and where time travel guys from the future warn Archer.