Craig Wighton’s exquisite strike 20 minutes from the end gave Hearts a hard-earned victory on their first visit to Gayfield on league business for 41 years.
But the well-organised home side could justifiably argue they should have had a least a share of the spoils.
Jambos boss Robbie Neilson was delighted with the result but admitted Arbroath proved to be worthy opponents.
He said: “I’m absolutely delighted. It was always going to be a difficult game against a really good team who have a great home record.
“But we are happy with the three points and we move on to the next game.”
Arbroath manager Dick Campbell added: “I’m unhappy with the result but not unhappy with the way we played.
“We sent out a clear message that Arbroath won’t be an easy game for anybody.”
The Lichties were without centre back Tom O’Brien who was suspended following his red card at Kirkcaldy last week but Colin Hamilton returned after injury while Kris Doolan and Michael Ruth were given starting berths.
Hearts made two changes from the side which started the demolition of Dundee, with Andy Halliday and Elliot Frear coming in.
As expected the Tynecastle side dominated possession in the early stages but it took until the 12th minute for the visitors to get a shot on target when Liam Boyce’s effort was easily gathered by Derek Gaston.
However, the expected onslaught failed to materialise and the loss through injury of the lively Josh Ginnelly seemed to upset the visitors’ creative edge.
Arbroath began to grow into the game and had a wonderful opportunity to take a shock lead when Doolan found himself free inside the box but Craig Gordon stuck out a foot to block the effort.
A few moments later Gavin Swankie had another chance but failed to make a good connection and Gordon saved easily.
The Lichties continued to impress and just before the half-hour mark Gordon again came to the Jambos rescue, brilliantly getting down low to push behind another Doolan shot.
Hearts created a few more openings at the start of the second period – Wighton was denied by a fine Gaston block before Frear curled a 20-yard attempt narrowly wide of the far post.
But the deadlock was finally broken in the 70th minute when Wighton, who enjoyed a loan spell at Gayfield last season, broke clear and coolly lobbed the ball over Gaston from the edge of the box.
Shortly afterwards Boyce came within inches of extending the Hearts lead with a shot that screamed narrowly wide.
The Lichties battled bravely to get back into the game and came so close to a last-minute equaliser when Ruth skimmed Gordon’s left-hand post.