Celtic scored in both halves to overcome a stubborn Dundee United side and move 16 points clear at the top of the Scottish Premiership.
Brendan Rodgers was keen to avoid a repeat of the goalless draw at Tannadice 17 days ago and stuck with the same starting XI that eased to victory against St Mirren three days ago, with Hyun-jun Yang drafted in for Nicolas Kuhn shortly before kick-off.
They dominated from the start and Daizen Maeda fired in the opener on the rebound to warm up the fans on a freezing night at Parkhead.
The visitors, who had some late chances, were well organized and frustrated the Hoops but Hatate came off the bench to fire into the roof of the net to secure another win for the hosts.
Celtic are unbeaten at home this season, while Dundee United remain third.
United pushed the hoops all the way
All smiles as Celtic extend their lead at the top of the Premiership
Rodgers has urged some fans to be more patient after they discovered a groan at back passes during his side's 3-0 win over St Mirren.
He also accused supporters in the standing section of disrespecting left-back Greg Taylor by chanting the name of transfer target Kieran Tierney.
The fans responded by repeating chants for the entire squad of other former players and manager Martin O'Neill.
Songs about Artur Boruc, Mikael Lustig, Billy McNeil, Charlie Mulgrew, Tommy Burns, Victor Wanyama, Jimmy Johnstone, Scott Sinclair, Jota, Odsonne Edouard and Henrik Larsson were broadcast.
Brendan Rodgers has urged Celtic fans not to disrespect Greg Taylor
The fans rounded off their back catalog with a burst of their song about Tierney, who is believed to be close to agreeing a deal ahead of a deal to return to Parkhead.
Jim Goodwin wrested little attacking energy from his players in a completely one-sided first half, but the visitors made a major defensive switch on 45 minutes that resembled an attacking and defensive training session.
The United boss would have been frustrated by the nature of the opener after his side appeared to have cleared Alistair Johnston's cross.
The ball fell to Luke McCowan just inside the box after Richard Odada fired a pass at shin level past Vic Sevel, and the former Dundee midfielder's shot deflected for Maeda to head home after being parried by Jack Walton.
Daizen Maeda opened the scoring for Celtic against Dundee United
Auston Trusty had earlier headed over the bar from one of Arne Engels' 10 first-half corners. The Belgian midfielder was Celtic's most threatened player, firing several teasing balls across the goal and coming close on several occasions.
United ended the half without a shot, corner or cross – Celtic had 27 – with just one touch in the home penalty area and 16 per cent possession.
There was rapid improvement after the break, although Kai Fotheringham and Glenn Middleton were wide of the mark from the first goals.
Reo Hatate doubled Celtic's lead
Celtic had chances to end the game earlier than they did. Taylor's cross was deflected wide by Maeda and United goalkeeper Jack Walton parried a substitute Kyogo Furuhashi header from Engels' second corner.
Kasper Schmeichel pulled off his first save in the 70th minute, tipping Middleton's powerful shot wide of his near post and soon after meeting Fotheringham's header.
The game remained in the balance until Hatate headed the ball into the top corner after fellow substitute Paulo Bernardo had invented Maeda's break.
Rodgers is delighted with the win as he awaits Kuhn's predictions
Use the Chrome browser for a more accessible video player
Celtic boss Brendan Rodgers was full of praise for the support of the fans in their 2-0 win over Dundee Utd.
Celtic manager Brendan Rodgers speaking to Sky Sports News:
“A good win for us. I thought we might have dominated the game.
“In the first half we had opportunities to score more goals and then in the second half we didn't quite score the second goal. So you have to go through a little spell where there are direct balls and long crosses, you have to deal with that.
“There was a bit of pressure but I thought the players handled it really well and got through it.
“Then we got the second goal and that eases our nerves that could be in the game. We fully deserved it, we worked hard and got a reward for it.
“I thought the atmosphere was great, regardless of the temperature, it was very, very cold, but they showed up in their numbers, the Celtic fans.
“They are amazing and give the team support and encouragement when needed and that helps us get the result.”
On Nicolas Kuhn's absence, he added: “He just felt something in the warm-up so unfortunately he had to come out.
“He didn't feel he was fit to play, so we'll assess that tomorrow and see where that is.”
Goodwin: Really tough question
Use the Chrome browser for a more accessible video player
Dundee Utd manager Jim Goodwin says the club is
Dundee United boss Jim Goodwin speaking to Sky Sports News:
“We knew tonight was always going to be tough with the amount of games we've had in recent weeks.
“Tonight is actually our sixth league game in the space of 17 days, so it's really difficult to ask the players to come fresh. It's hard enough at the best of times, but to come here two days after the Hearts game with very little recovery, it's always going to be difficult .
“The players gave everything, but unfortunately we just didn't do enough.
“We had opportunities to get the ball into the box with a couple of deep free kicks and a couple of long throws and we got a couple of corners but unfortunately nothing was too kind to us in and around the box.”