David Lowe's young side had ended 2013 with an impressive 3-1 victory over Manchester United and returned after the Christmas break to claim another three points.
Modou Cham, a goalscorer in the win over United, bagged two on this occasion as Rovers came from two goals down to clinch victory in the last minute.
Rovers started strongly in the north east, yet they found themselves two goals down inside 15 minutes.
The home side opened the scoring on ten when a cross from the right was well finished, before good combination play saw Boro net a second five minutes later.
On 20 minutes Rovers got a goal their play had deserved, Sam Joel sending a free-kick towards the back post to where central defender Sam Lavelle grabbed his first goal of the campaign from close-range.
Rovers pressed for more and eventually grabbed a merited equaliser just before half time. Modou Cham raced down the left flank before cutting inside onto his right and striking it beyond the goalkeeper.
Level at the break, it was Boro who were the better side in the second half as Rovers struggled to get their passing game going, giving up possession on too many occasions.
However Rovers defended manfully under pressure and their spirit was rewarded in the 90th minute when Cham netted his second with a carbon copy of his first.
Again the attacker raced down the left before cutting in on his right and the youngster fired home to seal the points.
"We really didn't deserve to be 2-0 down so early but we showed a real competitive edge to get it back to 2-2 in a first half that we didn't want to end," said Lowe.
"We struggled in the second half and couldn't get our passing game going but we defended manfully and managed to sneak a winner late on.
"It is a good start to 2014 for us."
ROVERS: Williams, Vicars, Doyle, Butterwick, Lavelle, Pierce, Harris, Wassi, Rittenberg, Joel (sub Tanner 66 mins), Cham.
Subs not used: Torres, Langford, Wall, Edgar.