Pakistan was caught by surprise as they did not expect a full invasion of Pakistan by India. India attacked regions that Pakistan least expected to be attacked; this was credited to better tactics by better officers employed by the Indian military and deserves at least some praise.
But again; surprisingly - halved garrisons managed to halt the combined Indian invasions, all though the Indian forces had successfully captured some Pakistani territory; the conditions and circumstances for the Indian forces was looking bleak, if they'd stay any further - it would've turned into a logistical nightmare (similar to Napoleon's invasion of Russia).
Any strong counter-attack; and the Indian lines would've easily been broken. Reversing Indian gains and paving the way for an invasion of Indian Punjab. The Indian Army had gambled all it's momentum on Punjab; a short term victory but what would've turned into a long term defeat.
As Pakistan was slapped awake; massive reinforcements were grouping to counter-attack Indian forces in Pakistan. Not to mention: armed tribes from both sides of the Afghan-Pak border were preparing for an invasion of IOK.
Indian forces which were facing logistic problems and were completely worn out by stern resistance, wouldn't have stood against the upcoming counter-attack. What India spent most it's strength on, Pakistan was just warming up.
But would it be worth it? Pakistan knew, due to international pressure; it wouldn't be able to hold onto any territory in Indian Punjab and invading Kashmir in the current circumstances would be a huge gamble (risked further losing territory in Punjab).
By the time the arrow was drawn; the ceasefire was signed. Pakistan had successfully held off the Indian forces in Punjab and won over majority air superiority - meanwhile India had made gains in Punjab, countered the incursions in Kashmir and destroyed a half of Pakistan's armored corps.
I would say no one won. Although India had a slightly more favourable stance near the ending of the war; that situation would've quickly changed if the war continued.
I highly doubt that; but even so - Pakistani pilots were better trained and more experinced. Even in air-to-air they were very much superior.
This was an interesting BBC interview to a group of Pakistani pilots who had just finished shooting down over a dozen Indian jets.