Greg Smith and Jaik Mickleburgh dug in to help Essex maintain their unbeaten start to the season.
It was another tricky one for Essex, who lost another fast bowler to injury and ended up 152 runs behind on first innings.
Three quick wickets on the final afternoon did leave a slight question mark but James Foster and Kishen Velani saw Essex to a draw.
Chosing to bat first, Essex found it tough going on the first morning, with Tom Westley (15) and Jaik Mickleburgh both scoring at a rate just over one run every five balls.
But that laid the foundations for Mark Pettini (71) and Foster (82) to push on, and Essex eventually made 281.
Debutant Oliver Newby took a wicket with just his second ball for the county, dismissing Matthew Boyce for two, but Tymal Mills soon had to leave the field with a side strain, and Leicestershire took advantage.
Their Greg Smith scored 59 in a 114-run partnership with Ned Eckersley, who then put on 149 with Angus Robson for the third wicket.
Essex's other debutant Tanveer Sikandar (2-90) finally broke that partnership by trapping Eckersley for 110, while Robson became Monty Panesar's second victim.
Josh Cobb added 70 but Essex - led by Panesar - kept going and the England spinner ended with 6-111 from a mammoth 50 overs as Leicestershire were bowled out for 433.
Westley fell early in the second innings, but Mickleburgh (67) and Smith (85) got Essex back in front.
They and Pettini fell in fairly quick succession and Leicestershire may have had a sniff of victory, but patient innings from Ben Foakes (17), Foster (41no) and Velani (21no) secured the draw.
Coach Paul Grayson said: "It's been a tough week, we've had a huge amount of injuries so it's nice to get through it with a draw.
"We showed a lot of character. Leicester are a good side this year, they gave us a good game.
"It's always tough when you've got two debutants playing, and then Millsy was injured as well so we went down to a three-man attack.
"I thought they did really well, maybe at other times teams might have got away from us.
"Monty bowled brilliantly and showed his class and hopefully he will get picked for the first Test."
