Best, playing his second match for the second string since returning from a lengthy absence due to his cruciate knee ligament injury, fired the opening goal at Rockliffe Park but the home side ran out winners courtesy of a second half Luke Williams hat-trick.
Gary Bowyer's side were late to arrive in the north east due to heavy traffic and it showed as they started the match slowly.
Just three minutes were on the clock when 'keeper Sebastian Usai was called into action, saving well to deny striker Wilson Kneeshaw after he was allowed to turn in the area.
On 13 the home side rattled the woodwork following a free-kick. Luke Williams' set-piece beating Usai but not the frame of the goal as the ball bounced off the crossbar.
Then on the half hour Williams went close once more with a free-kick, Usai showing sharp reactions to deny the striker.
As the half wore on Rovers came more into the game, ending the first 45 strongly.
After Anton Forrester had seen an effort saved, Jamie Maclaren fired into the side-netting when well placed, but the best chance of the half fell to Leon Best, taking the ball in his stride only to see his placed shot from the edge of the box tipped onto the post and behind by Connor Ripley in the 'Boro goal.
Raheem Hanley was then a whisker away from the opener with a fearsome shot, the midfielder's effort taking a deflection as it flew narrowly over the bar.
On the stroke of half-time it was the home side who threatened once more, Kneeshaw denied by an outstanding one-handed save from Usai. The Australian showing great reactions to push the ball over the bar from close range.
The second half saw Rovers start the stronger of the two sides, Jamie Maclaren being denied when his shot was tipped over before Leon Best, who was increasingly playing a key role in proceedings, saw a header from close-range cleared off the line.
The pressure told however as Rovers took the lead on 55 minutes. Raheem Hanley racing through the centre of midfield before laying the pass onto Best and he cooly slotted home from 12 yards.
But the lead was to last just four minutes as the home side soon equalised. Luke Williams was given far too much space as he advanced towards the edge of the area before lashing a superb strike beyond Usai.
Rovers looked to get regain their lead once more, Forrester saw an effort saved whilst Jamie Maclaren opted to pass rather than take the shot on when racing through.
Leon Best almost grabbed a second on 75 minutes when he poked goalwards from close-range but Andre Bennett made an important clearance.
With 13 minutes remaining Leon Best made way, the striker having done well with his 77 minutes of action.
After that match could have gone either way but with eight minutes to go it was the home side who grabbed the decisive second goal.
As with their first Williams was allowed far too much space, approaching the area he let fly once more steering the ball beyond Usai into the far corner of the goal.
The young striker claimed his hat-trick when Middlesbrough were awarded an injury-time penalty kick after the referee ruled that Will Beesley had handled in the box.
Williams stepped up and saw his spot-kick saved by Usai but the rebound fell nicely and he needed no second invitation.
BORO: Ripley, Bennett, Reach, Waters (sub Rhoden 79 mins), Burgess (c), Jackson, Brobbel (sub Fewster 79 mins), Morris, L Williams, Kneeshaw, Jones.
Subs not used: Montgomery (gk); Sirrell, Burn.
Goals: Williams 59, 82, 90 mins.
ROVERS: Usai, Wylie, Beesley, O'Sullivan (sub Payne 80 mins), Fernandez, Daly (c), Maclaren, Hanley, Forrester, Best (sub Hands 77 mins), Fabio Nunes (sub Pero 77 mins).
Subs not used: Urwin, Brown.
Goals: Best 55 mins.