This comfortable win made it two wins from as many games for Boro's new Swedish boss Kim Hellberg.
His side completely outclassed the woeful hosts in the first half to leave the match over as a contest before the interval.
Strelec finished smartly after Whittaker got first contact on a McGree cross from the left and the ball landed at the Slovakian international's feet.
The Tigers did not manage a shot of any sort in a horrible opening period and fell two behind when Gilbert, making his first appearance of the season, hit a quality low strike beyond Ivor Pandur in the home goal after lacklustre defending.
Gilbert then set up Whittaker to cut inside from the right and fire a third minutes later, although the Tigers were perhaps a little unfortunate as the Boro midfielder may have fouled Regan Slater in winning the ball on halfway.
The passive hosts could have no complaints at the fourth goal, though, as they allowed the visitors to pass through them with ease and McGree was able to score at the second attempt.
Boro, understandably, dropped off in the second half and Gelhardt pulled a goal back after visiting keeper Sol Brynn caught him in the area, although the contact seemed minimal.
Middlesbrough will look to build on this when they travel to out-of-sorts Charlton on Tuesday, 9 December (19:45 GMT). Hull, who would have gone third with victory on Friday night, will aim to put this dismal showing behind them when they host Wrexham on Wednesday, 10 December (20:00 GMT).