The hosts were always on top at The Riverside, but Hastings had their moments as they gave their 1,000 travelling fans a day to remember.
Boro - who went into the game with 13 first-team players out through illness and injury - should have gone ahead early on through Ishmael Miller after he was fouled in the box, but he saw his spot-kick saved well by debutant on-loan goalkeeper Liam O'Brien.
But it was not long before Middlesbrough did go ahead and it was a wonderful curling effort from Merouane Zemmama.
Hastings pushed on and created a couple of chances before the break with Jamie Crellin having a shot charged down before Bradley Goldberg's effort was ruled out for offside.
Boro then took control with a second goal which came just minutes after the restart when Hastings failed to deal with a corner which allowed Andy Halliday to fire home from close range.
A third followed on 68 minutes when Zemmama claimed his second although it was slightly fortunate as his shot took a massive deflection and left O'Brien helpless in the away goal.
Then from the kick-off, the moment all the Hastings fans had been waiting for arrived when they found the back of the net and it was the pick of the day as Goldberg let fly from 30 yards into the top corner - a brilliant piece of skill which earned equal applause from the Boro fans.
It was clear by their celebrations just how much the goal meant to Goldberg and the 1,068-strong army of travelling fans - just two off a remarkable 1066 coincidence - who had provided most of the atmosphere in contrast to the sparsely populated home sections.
There was still time for Boro to further add to the score-line and it came five minutes from time when Miller slotted home to seal a deserved and comfortable victory for the home side as they avoided a huge giant killing - but it was Hastings who rightly took the plaudits on the final whistle.