Stelios Giannakopoulos scored a dramatic stoppage-time equaliser to leave Bolton's UEFA Cup hopes on a knife-edge.
This was their third successive draw and they may need a victory against Red Star in Belgrade next Thursday to progress.
Yet with the clock running down at the Reebok Stadium Bolton were heading for the exit door.
Greece winger Stelios then made his mark to score only his second goal of the season and stun his fellow countrymen. A goal from Calvo a minute before half-time put Aris in the driving seat.
The visitors made their intentions clear as early as the seventh minute when Sergio Koke headed wide following a cross from Neto. They knocked the ball about with the confidence of a side that had lost only one out of nine league games.
Bolton carved out a half chance in the 22nd minute when Gerald Cid released Kevin Davies but his header was deflected to safety.
Aris responded immediately and Siston curled a shot wide when he should have at least tested goalkeeper Jussi Jaaskelainen.
A nice one-two between Mikel Alonso - who replaced the injured Gavin McCann - and Stelios saw Davies presented with a header at the back post. But he was unable to get enough power on his effort and Konstantinos Chalkias was able to make the block.
Alonso was working hard trying to create openings and rattled in a drive from 25 yards in the 37th minute that cleared the bar. Then Danny Guthrie floated in a corner three minutes later but Davies could not get enough direction on his header.
Aris took the lead a minute before the break through Spanish forward Calvo. He latched onto a clearance from Abdoulaye Meite and smacked a half-volley beyond Jaaskelainen.
Bolton, however, almost equalised in stoppage time when Andy O'Brien's header came back off the bar after Davies had flicked the ball on. They again came close in the 52nd minute when Alonso's powerful shot was blocked.
The loose ball was picked up by Guthrie and he delivered it into the area. Davies was unable to get a good connection, however, and Chalkias made a comfortable save.
It was a good spell of pressure by Bolton, despite another disappointing gate for a UEFA Cup match - 10,229. Aris were again forced on the back foot in the 64th minute when Giannakopoulos picked out Nolan but he steered his effort wide of the post.
Megson made a double substitution a minute later, bringing on Nicolas Anelka and El-Hadji Diouf for Christian Wilhelmsson and Davies. Meite then headed wide in the 68th minute after Diouf had delivered the ball from the right.
Bolton swept forward again in the 79th minute when Anelka squared the ball to Nolan. He tried to place his effort beyond Chalkias but only succeeded in finding the wrong side of the post.
Aris nearly extended their lead in the 82nd minute when Nacho tried to chip Jaaskelainen but the goalkeeper clawed the ball to safety.
Bolton grabbed a dramatic equaliser in stoppage time through Giannakopoulos, who scored from close range after Alonso had hoisted the ball forward. Aris were rocked but it was no more than Gary Megson's side deserved after a spirited second-half display.
