Basically, to the average viewer Pence won. But her's the problem, Pence was fighting the Battle--debating Tim Kaine directly--but Kaine won the war. What I mean by that is, the damage Tim Kaine did to the Trump Campaign will be lasting. He managed to reveal that Pence literally cannot defend his own parties nominee on the world stage. Pence had no answers for the things Trump has said, and at one point outright said "he's not a polished politician" which is the kind of thing that plays well to the Republican base, but for Moderate voters it's bad. Like, really bad. Now a lot of people were questioning this strategy, but I think it's because the Clinton Campaign doesn't think Hillary can go all in on attacking Trump in a debate like Tim Kaine can. Some of the points he brought up and Mike Pence didn't have answers for, will absolutely resurface in Sunday's debate.
The main thing about this is Pence's victory will be short lived. Reports are already coming out that Trump is not happy Pence "upstaged him", and once news networks start running their highlight clips, Kaine is going to sound like the definitive winner, because he has tons of good lines that just cut the Trump Campaign off at the knees. Kaine's main failing was that he was too anxious early on, and seemed almost Trump-esque for the first half of the debate, consistently interrupting Pence, who stayed pretty calm and collected during the whole thing. I will say, Pence maintained his cool, and he looked very professional compared to how Trump looked last week, and that might be why people feel like he won.
At the end of the day I can best describe it as Pence won the debate, and Tim Kaine didn't lose it. There were no "Gotcha" moments for Kaine, and he exposed a massive rift in the Trump Campaign, and kept the focus of the public on the people actually being voted for in November. Pence looked like a very respectable Republican Candidate, so people were alright with saying he won, but it's only because he was spending the entire time fighting against Kaine's attacks on Trump.