Celtic "will win the title" and are better than their rivals "in every single part of the team", said hat-trick hero Giorgos Giakoumakis after the dramatic late win over Dundee.

Ryan Sweeney levelled after the break for the visitors in Mark McGhee's first game in charge, but Celtic capitalised on Rangers' draw with Dundee United.

"We knew about the (Rangers) result, of course. It gave us a big motivation, but sometimes it gives you a little bit of pressure," Giakoumakis said after snatching a huge win in the title race.

"We showed that we are a better team, that is obvious. We showed that we work harder on the field and I hope and I think that we will win the championship.

"This squad is very good. I think it's the best in the league, we are better in every single part of the team."

Dundee remain two points adrift of St Johnstone at the bottom having played a game fewer.

Tensions rose inside Celtic Park as the league leaders bludgeoned their stubborn and well-organised visitors until Giakoumakis landed a massive 86th-minute blow.

The striker has been maligned a little since arriving at Celtic. He has spurned big opportunities, fluffed a penalty and been frustrated in front of goal, scoring four in 17 games prior to Dundee's visit, but his industry cannot be questioned.

The powerful 27-year-old is a workhorse and a relentless nuisance. He gets himself in tantalising positions over and over. His desire to get on the end of things never wanes no matter how wayward his finishing can be.

For a long time, it looked like it might be another troublesome day for Giakoumakis, who sclaffed an early shot wide from a smart Callum McGregor cutback. Celtic, in general, were laboured.

McGhee had bristled with indignation in his pre-match interview when it was put to him that some Dundee fans are underwhelmed by his appointment. He watched from the stand, serving the first of an outstanding six-game touchline ban.

In the early throes, his team did not so much park the bus as bring a fleet of double-deckers to Glasgow. And it worked as McGhee's five-man rearguard stymied Celtic.

The visitors had 14% possession and no shots when they struck out of nowhere. Celtic were bamboozled by a swirling Paul McMullan corner and, as everyone in green and white froze, Mullen side-footed past Joe Hart on the bounce from six yards out.

It was a stunning moment for the sparse band of travelling fans. Underwhelmed? More like over the moon.

But 64 minutes is a long time to resist a side that had rattled in 57 goals across 27 league matches. Dundee's lead evaporated after only eight.

Carl Starfelt's header ricocheted to Giakoumakis, who finished ruthlessly on the swivel from near the penalty spot.

Four minutes later, he was at it again. Daizen Maeda burned up the left flank and his vicious cross was parried to the feet of the striker by goalkeeper Ian Lawlor. Giakoumakis could scarcely miss.

There could have been a hat-trick soon after, when Giakoumakis was bodied to the ground by Vontae Daley-Campbell as a cross soared into the home box and the Celtic fans howled for a penalty. They kept howling as Maeda headed straight at Lawlor.

Celtic exploded into the second half, eager to blow Dundee away. Maeda missed another brilliant delivery and McGregor blasted over from a tantalising position inside the box. Jota blasted acrobatically home but was correctly flagged offside.

Dundee had scarcely touched the ball. As an attacking force, they were flatlining. And then, with help from Starfelt, the defibrillator was applied spectacularly.

The Swedish defender committed a silly foul, wiping out Niall McGinn. The former Celtic winger swung in a terrific ball from the right and the towering Sweeney bulleted home his header.

Sweeney's goal imbued Dundee with new belief and Mullen gave Celtic palpitations when he scooped a Max Anderson cutback over the bar at the near post.

Postecoglou sent for Tom Rogic and Liel Abada, two of his greatest creative talents. McGhee turned to Liam Fontaine, his most seasoned defender.

Abada would miscue a Jota cross wide. Anthony Ralston latched on to a deep delivery, but his volley was diverted clear. Jota skipped past half of Dundee before shooting tamely from the edge of the area.

It looked like a colossal, infuriating missed opportunity for Celtic and a tactical triumph for McGhee, until four minutes from the end.

Celtic Park was a boiling cauldron of frustration and angst when Giakoumakis answered the SOS call, slamming past Lawlor from inside the box with Celtic's 19th shot of the day.

Even then, there was time for more home distress as Dundee claimed furiously for handball with the final act.

But it would be a day for Giakoumakis to savour. After scoring the winner, he ripped his shirt off and twirled it vigorously around his head. Celtic Park went berserk. There is a long way to go yet, but the striker, and his fans, knew what a monumental goal it was.

Man of the match - Giorgos Giakoumakis

Three predatory striker's finishes from Giakoumakis earn three precious points

What did we learn?

Celtic's propensity for late heroics is nothing new, but it remains deeply compelling.

They had done it already to Dundee United, Ross County and Aberdeen - and their mental toughness to stick with Postecoglou's process when it would be easy to deviate from it has borne fruit.

Oddly, Dundee had taken the decision to sack James McPake after back-to-back wins, one at third-place Hearts and another at Peterhead to progress to the Scottish Cup quarter-finals.

McGhee has been widely pilloried since announcing his return to Scotland, but he had his team on the brink of a cleverly constructed draw.

With Dundee and St Johnstone picking up form, and Ross County's dipping a little, the coming weeks at the bottom of the table will be just as fascinating as the duel at the top.

What they said

Celtic manager Ange Postecoglou: "You can't get frustrated. You've got to stick to the process, that's where the answers lie. They don't lie in changing anything or losing our heads.

"After totally dominating the game, it's very easy for anxiety to build up, the crowd get a bit nervous, and we just had to stay calm and play our football."

Dundee manager Mark McGhee: "I was hoping we would have the bottle to get the ball down, to pass and run with the ball, and we did have good spells of that.

"That was the thing I was looking for as much as the effort, because I knew the effort would be there. The determination to do what we asked them was really encouraging."

What's next?

Celtic travel to Norway aiming to overturn a 3-1 Europa Conference League deficit against Bodo/Glimt on Thursday (17:45 GMT) with a place in the last 16 on offer.

Dundee host St Mirren a day earlier (19:45) GMT.