By beating Dundee they made it four wins and four clean sheets in a row.
Aberdeen may be eyeing top spot in the event of any further slips by Celtic, but they must also be making the occasional glance over their shoulders, where Neilson’s men are lurking menacingly with a game in hand and two head-to-heads still to come against the Pittodrie side.
It was a merited victory for the visitors, but a curious one in some respects, both sides contriving to miss some glorious scoring opportunities.
It is not as if either of them lack natural finishers and had some of them been in the mood the outcome could have gone either way and indeed we could plausibly have ended up witnessing a goal fest.
Jamie Walker, with his fourth strike in five games, was the man who made one count early in the second half to cap a fine afternoon’s work by a player who has added a new dimension to Hearts’ play since his return from injury. He may have been the first to contribute to the long sequence of scorned chances when he skewed an effort wide of the Dundee goal within the opening seconds, but he brushed it aside with his energetic performance thereafter.
Team-mates Juanma, Don Cowie and Arnaud Djoum could have broken the deadlock in the first half and with the visitors unable to add to Walker’s goal it was inevitable that there were moments when they lived dangerously. Dundee took to the field after the break with a renewed sense of purpose and went tantalisingly close through a couple of Paul McGowan efforts and an angled shot by Cameron Kerr.
In the closing stages Rory Loy also failed to get the better of Neil Alexander when through on goal.
With a top-three finish in the Premiership all but cemented, Neilson made no effort to disguise that he believes Aberdeen can still be overtaken. Captain Alim Öztürk agreed while admitting that they had at times made it hard for themselves over the 90 minutes.
“In the first half, we missed four 100 per cent chances,” he said. “We could have killed the game, but we didn’t. The second half we were alright, not as good as the first, but it’s a really important win. I think we can still catch Aberdeen. We have one game in hand and we will try. We look forward to the next game and try to win all our remaining matches.”
Unsurprisingly, he singled out Walker’s contribution, but also made a point of praising his defensive colleagues, all of whom were just 19 years old.
“I was the daddy today,” he laughed. “They did really well today. Another clean sheet and I’m really happy for them. We score almost every game so it’s really important to try not to concede goals – we are doing really well because of that.”
For Dundee there was some comfort to be had from their performance, if not the result, after their capitulation at Ibrox the previous week.
Manager Paul Hartley could rightly rue their own missed chances, but professed himself happy with how his players had applied themselves to steadying the ship and emphasised they still had ambitions of finishing as high as fourth.
Goalkeeper Scott Bain, whose call-up to the Scotland squad for the forthcoming international friendlies was announced last week, felt that he and his colleagues did enough to deserve a point from the game given the pressure and opportunities they had after the break.
There is little time to dwell on matters, however, with what promises to be one of the most crucial Dundee derbies in many a year looming large.
Bain was adamant that the story isn’t just about United’s plight.
“We need the points as much as them, we definitely do”, he insisted. “We need to be top six – that’s the only way that we’ll have had a good season. To beat them next Sunday will be a great step towards that.”