Scott McDonald scooped home the winner for Dundee United to keep them at the top of the Championship with nine points out of nine.
In truth, it was a difficult day for the Tangerines as they struggled to break down Brechin at Tannadice.
City did themselves and manager Darren Dods proud with a dogged display.
However, with just 10 minutes to go, the experienced Australian grabbed the only goal of the game to earn a close but crucial victory for Ray McKinnon’s men.
United had made a couple of changes to the team that started their last league game against Queen of the South.
Out went the suspended Paul McMullan and central defender William Edjenguele dropped down to the bench.
In for McMullan came Scott Fraser, while recent signing Paul Quinn partnered skipper Mark Durnan at the back.
That also made it a total of eight changes from Tuesday’s Irn-Bru Cup match against Cowdenbeath.
The Tangerines had plenty of the ball in the early stages without really hurting City.
The hosts would have grabbed the lead on 10 minutes were it not for a great save from goalie Graeme Smith, who finger-tipped away a Scott Fraser shot for a corner after he was found by a Billy King pass.
On 18 minutes, Andy Jackson almost got his head on a cross for City then the same player curled a shot beyond the far post.
Three minutes later, Jackson made it a hat-trick of chances for him and his team when he ran into the box and chipped the ball over keeper Harry Lewis. It was just off-target, though, and the danger was cleared.
Up at the other end, the Tangerines had a shout for spotkick when James Keatings went down following a challenge by Aron Lynas but referee Euan Anderson waved play on.
With 26 minutes gone, United defender Durnan stayed up after a corner and got his head on a Keatings cross from the left and it looked goalbound until it his City’s Finn Graham.
Ten minutes later, a superb pass from United’s Sam Stanton sliced open the Brechin backline and it looked like Keatings would reach the ball before Smith but the keeper did well to make the save.
On 42 minutes there was a real let-off for United as a Jordan Sinclair cross was kicked on to his own post by Durnan. Keeper Lewis then scooped the ball back on to the upright before it was eventually cleared by Durnan.
There was no question that Brechin boss Dods was the happier of the two managers at half-time.
United were needing to up their game in the second period but it was City who were creating the chances. Firstly, Jackson beat the offside trap and should have picked out the run of Kalvin Orsi.
Sinclair then brought a brilliant save out of Lewis with a volley from the edge of the box after Lynas’s cross. Next up Jackson, who was having a terrific match for Brechin, pulled his low shot wide of the far post.
Fraser found McDonald with a slide-rule pass on 61 minutes as United finally got back on the attack but the Aussie international pulled his left-foot shot wide.
The Tangerines made a switch on 61 minutes, bringing on Willo Flood for Keatings and pushing Stanton further forward.
A King corner was nodded past by Durnan at the back post as the hosts tried to make a breakthrough before Smith raced out to block a Murdoch shot.
City brought on Liam Watt for Euan Spark on 72 minutes, while United replaced an injured Fraser with Patrick N’Koyi four minutes later.
The home fans were, understandably, getting frustrated but they got the goal they wanted on 80 minutes.
Stewart Murdoch collected the ball on the right and took a touch before firing over a cross that landed at N’Koyi’s feet. The striker tried to get control of the ball but as he did so McDonald nipped in to scoop his shot into the net.
It was almost 2-0 but N’Koyi could only head past at the back post when in a great position..
City weren’t finished, though, and in stoppage time a terrific strike from Paul McLean just missed the United bar by a few inches.
However, the hosts held on to stay at the top of the pile.
Attendance: 6,060.
Dundee United: Lewis, Murdoch, Durnan, Quinn, McDonald, Fraser (N’Koyi 76), King, Stanton, Robson, Keatings (Flood 61), Fyvie. Subs not used: Deniz, Toshney, Edjenguele, Allardice, Chalmers.
Brechin: Smith, McLean, Dyer, Dale, Graham, Jackson, Lynas (C. O’Neil 86), Spark (Watt 72), Orsi, Crighton, Sinclair. Subs not used: P. O’Neil, Love, Layne, Ford.
Referee: Euan Anderson.