Kapur trailed the leaders by two shots after five birdies to shoot a six-under-par 66 at the Black Mountain Golf Club on his 33rd birthday.
Kapur, who was also fighting a cold, said: "It's a nice present. You wake up in the morning hoping for a good day because you don't want to be grumpy for the rest of the day. I couldn't have asked for a better result.
"They keep saying beware of the sick golfer and it seems to work. Hopefully I can stay sick and keep playing the way I am."
He added: "I think it's the early season rust. I felt like I play really well last week but go nothing in return in terms of results.
"It all comes down to holing a few putts. I got up this morning and I managed to do that. And that set the tone for the rest of the day. I'm looking forward to the rest of the week and also the year."