The only way this can happen is if you are a slow activator who is also fairly fatigue resistant (but in the example you mentioned, this might not be that important).
A neglected impact of going to failure is that it amps up the nervous system also as much as lifting heavy weights.
And in your case you did both: going to failure with heavy weights (low reps).
What creates what we call activation or potentiation of the nervous system is really the release of adrenaline which binds to its receptors in the brain and muscles. When adrenaline binds to the receptors in the brain it increases neuronal activation which will positively impact your capacity to recruit muscle fibers and coordinate your movements.
Several things can increase adrenaline levels when training. Intensiveness (how close you go to failure) and psychological stress (which includes the amount of weight you have to lift) are two of the main ones.
The closer you get to failure, especially on big compound movements, the more adrenaline the body produces. It senses that it might not be capable of continuing on with the reps. To increase your chance of survival, it will pump out adrenaline to increase your strength.
Now, with sets to failure, you also have to contend with fatigue, which will obviously decrease performance potential and it can negate (or more) the activation effect.
If someone has a lot of slow twitch fibers or has developed a lot of muscle endurance, the performance decrease from going to failure will not be as large and he could be able to do more reps even in the post-failure set.
I don’t think that’s your case.
What I think is that, YES you went to failure, but you went to failure with very low reps (4 reps on the first set). Hitting failure with low reps doesn’t have the same fatigue mechanisms as hitting failure with higher reps and doesn’t have the same negative effect on performance.
First, there will be no metabolite accumulation. Lactate and hydrogen ions will not accumulate with such a short time under load. Acidification of the muscle (by the hydrogen ions, NOT lactate, contrary to popular belief) diminishes contraction capacity (strength goes down) which decreases performance potential.
Sets of 4-5 will not yield that problem.
When it comes to failure on heavy/low rep sets, it is mostly due to the inability of the nervous system to make the recruiited muscle fibers maintain a high enough firing rate. It is also due to the depletion of phosphagens (ATP-CP) which occurs after around 12 seconds of intense effort. When you hit that point, your performance potential on high intensity contraction goes down slightly. Not enough to make you fail with light weights, but it can kill your set with heavy weights.
Those who things recover really fast. And since you are unlikely to create a large amount of muscle fiber fatigue with a set of 4 reps and because you won’t have metabolites to clear out, such a set doesn’t come with a large decrease in potential performance.
So activation from the adrenaline + low performance decrease = possible increase in performance potential.