Given the disarray in the Labour party and the fact that he's only done it once before, it was quite surprising this afternoon to see Jeremy Corbyn defeat David Cameron at PMQs. It wasn't a slam-dunk, or a knock-out blow, or any other definitive sporting analogy. It was a tight thing and perhaps Corbyn excelled on the basis of low expectations. But there were glimmers of very effective political attacks there and by the time the dust had settled, the Labour leader stood in the better position.

Corbyn still has plenty of weaknesses. He twice told the prime minister he could simply write to him in response. Prime ministers very often promise such a thing in PMQs but it is better not to direct someone off the hook you are holding if you would rather they stayed on it. He stumbles a bit and takes long pauses, all of which come across as highly amateurish to me, but the standard Corbyn health warning applies: what most journalists see as amateurish in the Labour leader is regarded as refreshingly authentic by his supporters.

Instead of using an email per question, Corbyn elected this time to strip down the number of contributions from the public, focusing first on tax credit cuts. Cameron is on the ropes on this one and Corbyn knows it. It contradicts his stated principles of supporting work. It is opposed by the Sun. Nearly everyone in Westminster expects a U-turn. There is a strong sense the Tories overplayed their hand.

Cameron replied by listing the measures he was taking to help low income earners, none of which would make up for the fact that the emailler was set to lose thousands of pounds. But Corbyn pushed him effectively.

The prime minister had a task today – to get Labour to fall into George Osborne's very obvious trap on the so-called fiscal charter. He was full of his standard demands for the opposition to join the government tonight or show the nation they were planning to borrow more forever. It was the usual guff he'd used very effectively against Ed Miliband for years: find a tiny hinge upon which to flip the party onto the wrong side of public opinion, and then make everything about that.

But Corbyn had his own little trick. He told the prime minister to come join Labour's opposition day debate on tax credits next week. It was a small thing – a standard strategic manoeuvre designed to increase the pressure on the prime minister on a subject where the leader of the opposition knows he's vulnerable. But it was the first time we'd seen Corbyn behaving strategically at all. Until now it has been values, values, values with nothing to drive them home. Finally there was an attempt to inflict damage on the prime minister.

It might have been less effective if Corbyn had not been so unfailingly polite. His tone – a complete negation of the usual yaa-boo of PMQs – is actually very effective against Cameron. Miliband tried to out-macho him, which never worked. Much better to play to your strengths and in Corbyn's case his strength is that he's really very likable. He sounded utterly reasonable and genuine in his concern. It made his attacks much stronger. Once again, it reminded us that he would benefit from doing more media interviews, rather than run from them.

The Labour leader left tax credits well before he should have done. Cameron was in a proper bit of bother there and he failed to notice it. And he failed to reiterate his observation yesterday that he had forced Cameron to think again on the Saudi Arabia prison deal. It is false – Michael Gove at the Cabinet table and David Allen Green in the press did most of the legwork on that one – but it would have complimented the tax credit demands nicely. Corbyn's just not quick enough on his feet yet.

But given that this is just his second PMQs, it was impressive stuff and a major improvement on his first go. He's already walking away from them a winner. Within a few weeks, he could prove genuinely dangerous to Cameron at these weekly encounters