The Serbian got his clay court season off to a positive start, breaking Montanes on two occasions as he claimed the opening set 6-2.
The second set appeared to be heading for a similar outcome as Tipsarevic served to win the match with a 5-2 advantage.
However, his Spanish opponent responded by claiming a break of serve to close the gap to 5-3.
Montanes failed to capitalise on his first break though, as he went on to surrender his next service game for Tipsarevic to claim a 6-2 6-3 victory.
Tipsarevic will now face Gilles Simon in the next round following the Frenchman's win over Frederico Gil earlier today.