The Magpies created the better chances in a tight first half and almost took the lead in the fifth minute when Nolberto Solano fired a rasping 30-yard drive against the crossbar with Francesco Toldo beaten.
Sir Bobby Robson's side had a scare three minutes earlier when Emre fired over the bar from a good position after being set up by Christian Vieri but they edged the opening stages and Toldo had to be at his best in the 19th minute to deny another Solano effort.
Three minutes later Jermaine Jenas jinked his way through the Italian defence but his final shot was weak and Toldo saved easily.
Inter hit back and Shay Given had to be alert to deny Javier Zanetti in the 25th minute.
However, Newcastle continued to create the better chances with Craig Bellamy going close to breaking the deadlock after some great play by Gary Speed.
With three minutes of the half left Newcastle took the lead as Bellamy created the chance for Shearer who made no mistake from close range.
Inter started the second half well and equalised in the 47th minute when Sergio Conceicao broke quickly before crossing for Vieri to head past Given.
Newcastle could have been rocked by the equaliser but they responded positively and restored their lead just two minutes later as a Toldo howler allowed Shearer to score his second goal of the game and 23rd of another magnificent season.
Given made a brilliant save from Vieri on the hour before Inter equalised for a second time in the 62nd minute as the Colombian international Ivan Cordoba powered a bullet header past Given.
Both sides continued to attack as they went in search of a priceless winner but the match ended in deadlock.
The result means United must beat Barcelona at St James' Park next week and hope that Inter fail to beat a poor Bayer Leverkusen side in Germany in order to defeat the odds once again and move into the last eight.