These are some of the methods I've used as a roughly 1600 rated one minute quick player to beat opponents often above 1750. These don't always work and can be risky. I will provide an example for each tactic convenient.
1: Choose an opening you are familiar with and know the general plan of how you want to play (pawn storm on the kingside, or queen and rook say mate on h7).
Even though my opponent played poorly in this game, and we both missed some moves, my plan worked.
2: Develop quickly, so that you can react to anything and carry out your own plan.
After this position, I went on to win the game.
3: Games generally tend to be more simple in quick games than longer, more thought-out games. So, always have a move that you want to play in your mind ahead of time (Nf3 for example) and hover your mouse with the piece over that square already.* Then, when your opponent moves, all you have to do is make sure there are no threats and let go of the mouse. Think on your opponent's time, not yours.
4: Use premoves. Premoves allow you to make a move ahead of time, before your opponent moves. This will make your time go not go down at all, or only by a tenth of a second. Premoves are played as any other move, but only before the opponent moves. If this doesn't work, check under settings to enable that option. Often, premoves don't work on the first try.*
a: Safe premoves include repcapturing in case the opponent captures. If he doesn't capture, the premove doesn't work because you can't take your own piece. In the endgame, some premoves are also safe, sometimes including advancing a passed pawn.
b: Unsafe premoves include nearly any other moves. However they can be the difference between victory and defeat in time-pressured endgames.
c: Etiquette of premoves are very important in the endgame. Whether winning or losing in position, what premoves you make are vital. When losing by a queen or rook in the endgame, always flee with your king to move out of the checks that are likely to come. Likewise, when winning in position, try to check the opponent as much as possible to nullify most premoves he has made.
5: Never resign. There's always a chance your opponent will blunder or run out of time, or stalemate you, or even disconnect so just keep on playing.
6: Cheap tactics. These should only be used against friends or if you have no conscience. Type "Hi, how are you doing?" before you play your first move, so that he might get distracted. If you see that he will checkmate you in one, and he only has a second and you have a minute, wait until the last few moments before playing your final move. He may be caught off guard and not play his move in time.
General gameplay: Your opponent will often strive to achieve a single position that he is familiar with (see game 2). Also, there will be fewer exchanges, as calculations of whether or not the capture is safe takes up valuable time. Keep it complicated if you are winning on time, and have a lower rating or are losing in position. Make your opponent think before he gets to win.
*If you can't play that move, simply right click before letting go of the left click. This will return the piece to its previous position (or remove the premove).
Well, those are all the tips I've got. Hope this helps you win some more games. Any comments or suggestions are welcome.