I don't have a huge amount of experience with this game yet, but if I'm understanding the manual correctly, an influence victory requires you to have 75% of the galactic influence and
sustain that amount for 10 turns. Therefore, I assume that if your influence amount drops below 75%, you won't win by influence victory unless it goes back above. So, yes, taking either Moosetek's or Mystikmind's strategies should work to stop the influence victory from happening.
Or, depending on how close you are to another kind of victory, you might have the time to finish up the game in another way before the 10 turns is up. I was playing a game recently on Cakewalk (to see, after beating Normal, how much better I could do than Cakewalk computers
), and suddenly the message popped up that I would win by influence in 10 turns. I was planning on a military victory so I just hurried about 20 Advanced Transports (my own design), then sent them toward each of my opponents' planets. Their movement speed was high enough that it didn't take any of them longer than about 7 turns to reach the planet I sent them toward, so I managed to win by military despite my high influence.
On second thought, if I'm not planning on winning by influence, I should probably turn that victory type off...
