Claudio Reyna returned to competitive action by coming through the first half unscathed, when Boro’s Daniel Graham netted the game’s opening goal.
City went close with Ian Bennett striking the top of the crossbar from distance, before the visitors’ top scorer Graham beat Paddy McCarthy in the box to fire past Weaver in the 27th minute.
But Weaver then denied Boro’s Andrew Davies and saved a 30-yard free-kick from David Wheater.
Weaver’s former City understudy, Carlo Nash, was in goal for Boro and managed to save bravely from Willo Flood, but City’s equaliser came when Bradley Wright-Phillips, the nation’s top reserve scorer, took his tally to 15 with a glancing header from a left-wing Paul Collins cross.
The drama didn’t finish there though, with Weaver diving to his right to deny Graham an injury-time match-winner.
City: Weaver, Warrender (Lee-Matthews 90), Collins, J D’Laryea, McCarthy, Bischoff, Flood, Reyna (C Logan 45), B Wright-Phillips, Bennett, Croft.
Subs: Ellegaard (gk), Laird, Tandy.
Boro: Nash, McMahon, Taylor, Wheater, Bates, Davies, Peacock, Parnaby, Graham, Kennedy, Johnson.
Subs: Knight (gk), Craddock, Clough, Hines, Lemaire.
Attendance: 505.