Gianluca Mancini's own goal denied José Mourinho's Roma a first-leg lead after Lorenzo Pellegrini's classy opener.
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The sides could not be split after an engaging first leg of this UEFA Europa Conference League semi-final.
15' Pellegrini caps fine move for opening goal
67' Mancini turns Barnes' cross into own net
Match in brief: Leicester battle back for draw
Leicester, making their European semi-final debut, started the stronger of the sides and forced a number of early corners. The best of James Maddison's set piece deliveries picked out the run of Timothy Castagne to the far post, but the Belgium international was unable to direct his powerful header towards goal.
However, Roma grew into the game and took the lead with a sweeping attack. Switching play from the right flank to the left in their own half, Nicola Zalewski powered down the wing before threading a delightful pass through the Leicester defence for the run of visiting skipper Pellegrini, who slotted his finish through Kasper Schmeichel's legs.
The Foxes began the second half on the front foot and almost capitalised when Marc Albrighton's inswinging corner picked out Ademola Lookman in space, but the 24-year-old mistimed his jump, heading over as a result.
Just as in their quarter-final second leg, some changes in personnel midway through the game paid dividends for Brendan Rodgers. He introduced Harvey Barnes just after the hour mark, and it was the midfielder who played a key role in the equaliser five minutes later. Barnes burst into the Roma box before cutting the ball back for Lookman, but Mancini, in his haste to get to the centre before the Leicester player, could only help it into the Roma net.
The home side sensed victory and only a stunning save from Rui Patrício prevented sub Kelechi Iheanacho's curling effort from nestling in the corner of the net.
Joe Terry, Leicester reporter
A much better second-half performance from Leicester, who took advantage of Roma dropping deeper and deeper to claw themselves better into the game. Given their dominance in the second half, they may even be kicking themselves for not going one further, but as it stands this tie is finely poised. Roma will back themselves at home, but as the last tie showed, Leicester can hurt anyone.
Francesco Corda, Roma reporter
Roma were unable to capitalise on the early goal against a Leicester City team that seemed a little bit sharper. Just as inertia appeared to be setting in for José Mourinho's men, Rodgers' changes breathed new life into the Foxes, who were good value for this draw. It's all open for the second leg, where the Giallorossi will need Tammy Abraham and Nicolò Zaniolo at their best.
Brendan Rodgers, Leicester manager: "I thought we played ever so well. We really dominated the game. They've got dangerous players but I'm very pleased with the performance. You come into a semi-final and you want to start well, bring your tempo and intensity into the game. The only thing missing was the final bit of quality in the final third."
Ademola Lookman, Leicester midfielder: "There were times where we broke them down. We created the chances, but it's unfortunate we couldn't get the win. It's going to be a difficult game in the second leg with the atmosphere and their fans behind them. We'll go there to try and win."
José Mourinho, Roma head coach: "I think we would have lost this game five or six months ago. We had the courage to start strongly, pressing hard and leaving them little space. Then our energy levels lowered, we conceded a goal that we could have avoided and now there will be a final at stake in Rome."
Lorenzo Pellegrini, Roma captain and goalscorer: "We knew it wouldn't be easy coming here. They're an excellent team, so we're pleased and fired up to go again. Coming away from here with the score at 1-1 ahead of the second leg at home is certainly a plus for us. The way we approached the game this week should serve as the template for next week."
- Roma have scored in their last 23 UEFA club competition matches.
- Leicester have lost just one of their last 17 European home matches.
- Roma have won just one of their last 19 UEFA trips to play English opponents away from home.
- Ten of Leicester's 13 goals in the UEFA Europa Conference League have come in the second half of matches.
Leicester: Schmeichel; Ricardo Pereira, Fofana, Evans, Castagne (Justin 21); Maddison, Tielemans, Dewsbury-Hall; Albrighton (Barnes 62), Vardy (Iheanacho 62), Lookman (Pérez 83)
Roma: Rui Patrício; Ibañez, Smalling, Mancini; Karsdorp, Mkhitaryan (Veretout 57), Cristante, Pellegrini (Afena-Gyan 85), Zalewski (Vina 85); Zaniolo (Sérgio Oliveira 69), Abraham
Tirana's National Arena (Arena Kombëtare) will stage the final on Wednesday 25 May.
The winners gain a place in the 2022/23 UEFA Europa League group stage, if they have not qualified via their domestic competition.