M-Sport Ford's Estonian driver Ott Tanak (35) won five of the day's seven stages and would have led on outright pace, however, had he not been handed a five-minute penalty for a change of engine on Thursday.
Championship leader Rovanpera won the other two stages in the afternoon to reel in Neuville after the Belgian built up a 6.8-second lead by lunchtime on the fast gravel roads around Tartu.
"I’m definitely satisfied to finish the day in second place. We would like to have kept our first position but we expected Kalle Rovanpera to be very fast this afternoon," said Neuville.
"Tomorrow will be tough, Kalle has the better road position if there is no rain, so let’s see what we can do."
Hyundai's Esapekka Lappi (32) was third, 12.2 seconds off the pace.
A further nine stages are scheduled for Friday.
