If you are flying along normally you will have some angle of attack which results in the wing lift's providing almost all the upwards force value necessary to balance the weight of the aircraft. The propeller thrust force is pointing somewhere out to the front but, generally, with a small inclination upwards. This inclination results in our being able to figure that the major part (horizontal component) of the thrust is sorting out the drag, while a little bit (vertical component) is attending to providing a small part of the total vertical force needed to balance that last bit of the weight force.
Now you can juggle the situation in various ways but, at the end of the day, you need to have the sum (total) of the upwards acting (vertical component of the) wing lift and the upwards acting (vertical component of the) propeller thrust force being equal to (and balancing) the downward weight force.
You can increase/decrease the vertical thrust component by increasing/decreasing the power setting. If you want to keep flying straight and level, though, if you increase/decrease the vertical component of the thrust force, you will (necessarily) have to decrease/increase the vertical component of the wing lift force so that the total of the thrust and lift vertical force components continue to add up to the weight force. If you don't do this, the aeroplane is either going to climb or descend according to whether the total upwards force (lift and thrust components) exceeds, or is less than, the downwards acting weight force.
You have no choice there, if things are not balanced, there will be an acceleration. The same sort of argument applies horizontally - if the forces don't balance out, then you will necessarily have an acceleration which either increases or decreases the aeroplane's speed.
Now, we said that we can increase/decrease the thrust force by increasing/decreasing the power setting. We can change the wing lift bit by changing the angle of attack (think back to the graph of lift coefficient drawn against angle of attack). So, presuming we want to fly level, if we do something to increase the vertical thrust component, then we must do something to reduce the vertical wing lift force component. So we pitch down a bit, the angle of attack reduces and the vertical component of wing lift force reduces. Providing the total of the wing lift upwards force component and thrust upwards force component continue to add up to the weight force value, we will continue to fly level.
But this means that we are now further away from (below) the stalling angle of attack. If we want to, we can pitch back up to increase the angle of attack, which will decrease the speed. If we keep pitching up, we eventually get to the stall (but now at a lower speed than with idle thrust). We can continue this argument until we are at full power (maximum thrust) with a quite measurable reduction in the stall speed at the maximum thrust setting when compared to the idle thrust situation.
Consider an extreme situation - you have an engine/propeller combination which has enough grunt available to produce a thrust equal to the weight of the aircraft. Providing that you can address any stability considerations, you would be able to pitch to the vertical and hang there on the thrust force with the wings having a total holiday. Stall becomes irrelevant in this situation.