The Serbian raced into a 4-1 lead early on, showing his class with some excellent ground strokes, and eventually took the first set 6-3.
Lacko, still confident from his impressive first-round win, improved in the second set, working his opponent hard in punishing rallies.
He missed the chance to break the number eight seed at 4-3, hitting a difficult forehand long, but continued to unsettle Tipsarevic.
Some impressive play at the net appeared to give the Slovakian the upper hand in the next game, but a double-fault at 40-0 allowed Tipsarevic back in, and he eventually broke Lacko's serve.
Tipsarevic was made to work in his final service game but took the set with two accurate forehands for a 2-0 lead.
Lacko recovered from a break down, mixing powerful ground strokes with clever play at the net, to take a 3-2 lead in the third set.
He seemed to throw caution to the wind after that, setting up another break point with a fantastic backhand down the line. He duly won the game to love before holding serve for a 5-2 lead.
Tipsarevic did force his to opponent serve out the set, but Lacko was unnerved, finishing with an ace.
The fourth set began on serve, with neither man wanting to take too many unnecessary risks as they started to tire.
It was Lacko who made the breakthrough though, smashing a second serve back past Tipsarevic to break, before saving two break points to hold his serve for 4-2.
The set continued on serve, with Lacko looking stronger and stronger as he took the match into a decider.
The long baseline battles continued in the final set, with both men managing to hang onto their own serves early on. It didn't take too long for a break though.
Having taken an injury timeout, Tipsarevic looked revitalised and broke his opponent, who himself was looking increasingly troubled by an Achilles problem.
Tipsarevic pushed home his advantage and made it 5-3, only for Lacko to dig deep and break back, saving two match points in the process.
It wasn't long before Tipsarevic had another, setting it up with an incredible forehand pass and taking it with a cross-court backhand to win the set 7-5.
Tipsarevic will face Julien Benneteau in round three.