Stephan El Shaarawy's first-half goal looked like it might be enough for Roma to return to winning ways upon the resumption of the league following a brief winter break, but Vecino denied the visitors all three points at San Siro to keep Inter three points above their opponents in fourth.
Roma have now failed to win any of their last five games across all competitions and remain outside the Champions League places, whereas Inter are winless in their last eight outings having led the way in Serie A a little over a month ago.
Inter's form has seen them slump from title challengers to facing a battle for a top-four spot, but the hosts had the first clear chance of the contest this evening when Ivan Perisic was denied by Alisson from close range shortly before the half-hour mark.
Alisson was involved in an attacking sense for the opening goal moments later when his long pass forward beat the entire Inter defence to release El Shaarawy through on goal, and the winger burst into the box before dinking his finish over Samir Handanovic.
Clear chances were few and far between at both ends of the field as Roma attempted to keep their hosts at bay, and it wasn't until the 74th minute that Inter really threatened an equaliser.
Mauro Icardi met the ball inside the area with a first-time finish which had Alisson beaten, but his effort came back off the post as Roma survived.
Inter did finally level things up with just four minutes of normal time remaining, though, as Vecino rescued a late point for his side with a close-range header from Marcelo Brozovic's deep delivery.
There was no time for Roma to respond to that as the spoils were shared at San Siro, leaving Inter now nine points off leaders Napoli.
INTER MILAN (4-2-3-1): Handanovic; Cancelo, Skrinar, Miranda, Santon (Henrique, 77'); Vecino, Gagliardini (Brozovic, 46'), Candreva (Martins, 70'), Valero, Perisic; Icardi
ROMA (4-3-3): Becker; Florenzi, Manolas, Fazio, Kolarov; Pellegrini., Strootman, Nainggolan; El Shaarawy (Jesus, 74'), Dzeko (Schick, 84'), Gerson (Peres, 70')