The Portuguese teenager pounced with an early header which ended Oldham's cup heroics in a closely fought match at Boundary Park.
The underdogs could have forced a replay but found the Bolton defence in tight fisted mood and wasted the few chances which came their way.
Bolton were relieved to avoid the same fate as Manchester City, who were humbled by Oldham in round three, but their victory came at a price as defender Nicky Hunt was carried off with a suspected broken leg.
Sam Allardyce's men converted their first opportunity when Ricardo Gardner crossed from the left after nine minutes.
Vaz Te got in front of his marker ten yards out and powered a header which Oldham keeper Les Pogliacomi reached with his left hand but could not prevent crossing the line.
Oldham created a chance which John Eyre miscued and were also frustrated when Mark Hughes fired over the bar and Danny Hall sent his header the same way.
Kevin Davies was denied by Pogliacomi shortly after half-time before Hunt was left in agony after a dreadful challenge from Lee Croft, which the referee opted not to punish.
Vaz Te could have put the scoreline further in Bolton's favour but his side came under heavy pressure for much of the second period as the plucky League One side mounted a series of attacks.
Hall was kept out by a superb stop from Jussi Jaaskelainen and Alex Bruce volleyed over the bar from close range in what was to prove Oldham's last chance of another giant killing.