Latham smashed Colin Ackermann for six to reach his hundred but was caught behind off Neil Dexter for 124.
Opener Steel went on to make his century off 242 balls, before passing his previous first-class best of 128.
Dieter Klein claimed a couple of late wickets but Steel ended unbeaten on 145 as Durham closed on 324-4.

The "fully-guided" tours will take place at weekends, when the specially-built set on the Harewood Estate in Leeds is not being used for filming.
They will take in "the familiar haunts of Home Farm, Bob's Cafe and The Woolpack", a spokeswoman said.
She added they had been launched as a result of the "incredible success" of the Coronation Street tours.
About 850,000 visitors looked around the famous cobbled streets of Weatherfield before the tour was closed to allow redevelopment of the site.
Emmerdale moved to the purpose-built set in 1998 after the number of fans visiting its original location, the West Yorkshire village of Esholt, made filming difficult.
The new tours will take place on 10 Saturdays in April, July, August and October.
The head of ITV North, John Whiston, said the set was "a unique and special place", which the company were "excited to be able to show off to a select number of visitors".
Unlike those at Coronation Street, the Emmerdale tours will not offer the chance to see the interior sets, which are housed at studios near Leeds city centre.

Saunders has left Wrexham after three years to succeed Sean O'Driscoll at Doncaster Rovers.
Morrell will be in charge for Saturday's Blue Square Bet Premier game at Grimsby.
"I spoke to the directors on arriving at Colliers Park this morning and they have asked if I would take on the first team affairs," said Morrell.
Doncaster-born Morrell is in his second spell at the Racecourse after being re-signed by Saunders in June 2010.
The 35-year-old had originally joined the north Wales club from non-league side Newcastle Blue Star in 1998.
Morrell left the Racecourse to join Coventry City on a free transfer in 2003 before spells with Blackpool and Bury.
"I'm only too happy to help out," Morrell told Wrexham's official website.
"It's come a little bit earlier than I was planning but you can't turn down such an opportunity, they don't arise too often
"I feel I still have plenty to offer as a player and this will also allow me to see what life is like on the other side of the fence."
Morrell will be assisted by coaches Brian Carey and Michael Oakes for Saturday's trip to Grimsby Town.
Morrell scored a record seven goals for Wrexham in a FAW Premier Cup tie against Merthyr Tydfil
Saunders succeeded Brian Little as Dragons boss in October 2008 but Morrell said the job at Doncaster was one which the former Wales striker could not refuse.
"Personally I can only wish him well at Doncaster and thank him for all the help he has given me," said Morrell.
"But it's fantastic for him to get such an opportunity and it also reflects well on our club. "
Cameron Steel and Tom Latham shared a 234-run first-wicket stand as both scored centuries to help Durham dominate against Leicestershire.
[NEXT_CONCEPT]
Soap fans will be able to take a tour of Emmerdale from April, ITV have announced.
[NEXT_CONCEPT]
Wrexham have put striker Andy Morrell in temporary charge following the departure of Dean Saunders.