But a number of Leicestershire batsmen got starts and then got out as they lost wickets at regular intervals.
Debutant Callum Parkinson took 3-64 as four Leicestershire men were out in the 40s, before Eckersley's patient innings helped them rebuild.
He hit seven fours as Leicestershire ended the first day on 300-7.

Cooper, 31, was playing for Culcheth Eagles at Runcorn ARLFC and had been substituted when he began to feel unwell at the start of the second half.
An ambulance was called but they were unable to save the father of three.
Rugby Football League officials are supporting the family of Cooper and a donation page has raised over £8,000.
Culcheth Eagles junior sides played as normal yesterday, with all matches preceded by a minute's applause.
No decision has been made about whether the planned open-age league match at Cadishead Rhinos on Saturday will go ahead as planned.
"It is awful," said Culcheth Rangers' vice-chairman Jo Eland. "Adam was just a young lad going out to play the game he loved."
Cooper was a longstanding member of the club and returned from Leigh East to play with them when they re-established their open-age team in 2010.

"This battle is ours... and I promise you victory," he said in a TV address.
Syrian rebels in the besieged town of Qusair say they are under heavy bombardment from Hezbollah combatants.
The town is close to the Lebanese border, a conduit for both the government and rebels to get weapons.
In the speech from an undisclosed location, Mr Hasrallah said if Sunni Islamists took over in Syria, they would pose a threat to the entire Lebanese population - Shia and Sunni Muslims, as well as Christians.
He said his movement could never be aligned with Syrian rebels who, in his view, were supported by the United States and Israel.
Hezbollah plunges deep into Syria conflict
Dozens of Hezbollah militants are said to have been killed fighting alongside Syrian troops in Qusair since 19 May, when government forces launched an offensive to recapture the rebel-held town.
Last week, US Secretary of State John Kerry said thousands of Hezbollah fighters were contributing significantly to the violence in Syria.
He added that Iran was actively supporting Hezbollah's involvement - a claim denied by Tehran.
Iran and Hezbollah are predominantly Shia, while Mr Assad's Alawite sect is an offshoot of Shia Islam.
The week-long fighting in Qusair intensified early on Saturday, when activists reported heavy bombardments, including two ground-to-ground missiles and an air strike as well as artillery and rocket fire.
Syrian state media said the army had launched a three-pronged offensive in the north, centre and south of Qusair, and was making big advances after "killing large numbers" of fighters.
Qusair is important for the Syrian government because it links the capital, Damascus, with the Alawite heartland on the Mediterranean coast. However, official media made no mention of the part played by Hezbollah.
The Lebanese group is also known to have lost a number of fighters in Qusair, prompting Lebanese President Michel Suleiman to warn the Shia militia against getting "bogged down in the sands of discord".
The Syrian Observatory for Human Rights, a UK-based activist group that monitors the conflict, said at least 22 people including 18 rebels had been killed in the latest fighting in Qusair. Dozens had been wounded, it added.
Ned Eckersley hit an unbeaten 73 as Leicestershire enjoyed a decent opening day with the bat against Derbyshire at Grace Road.
[NEXT_CONCEPT]
A minute's silence will be held before every rugby league game this weekend in memory of amateur player Adam Cooper who died during a match on Saturday.
[NEXT_CONCEPT]
The leader of the Lebanese Shia militant Hezbollah movement, Hassan Nasrallah, has promised his supporters they will prevail in Syria, where they are backing President Bashar al-Assad.