Jack Muldoon had cancelled out Onariase's 16th minute opener but after Eisa's strike just before the half restored the visitors lead, his second and late strikes from Loft and Jarvis sealed an emphatic win.
Simon Weaver made one enforced change coming into the game, with Connor Kirby replacing the suspended Kevin Lokko and slotting in at right back in a revamped back four.
Scunthorpe had struggled for goals this season, tallying just eight so far and having failed to score more than one goal in all but one of their league games but did come into the encounter on the back of two consecutive away wins.
And it was the visitors who signalled their intent early when Onariase seized on hesitancy in the back four but couldn't control his header at goal.
The defender would get his reward on 16 minutes though when he bundled the ball home at the far post from a corner.
After falling behind Town were struggling to find a way to get back into the game and only an intervention under his own bar from Warren Burrell cleared further danger.
With his side creating little in the opening half an hour Weaver switched to a 4-3-3 formation, with Calvin Miller pushed further forward.
The change provided immediate dividends when Muldoon levelled on 35 minutes, meeting Mark Beck's powerful nod down to decisively hit home for his eighth league goal of the season.
This ignited a spirited spell from Town as they looked to completely turn the game around but their good work was undone minutes before the break when Eisa pounced on a defensive mistake to calmly slot home past Belshaw.
Despite a limited bench, Weaver made a change at the break with Brendan Kiernan replacing Kirby, with Calvin Miller dropping into a reshuffled back line.
Town struggled to impose themselves at the start of the half though, with the visitors content to hold their lead.
Their job was made even harder when they fell further behind after Eisa netted from the spot after Muldoon was harshly adjudged to have handled; the lengthy Town protests were evidence of the players frustration with the decision.
Weaver made his second change of the evening when Aaron Martin replaced Lloyd Kerry but a swift counter-attack on 74 minutes resulted in an unmarked Lofted netting a fourth and final goal for the visitors.
George Thomson's direct free kick forced a save from Mark Howard on 79 minutes but this was all Town could muster on goal.
Belshaw was then punished when his heavy touch presented substitute Jarvis with an easy finish to round off a convincing night for the Iron.
Connor Hall netted a late consolation for Town, but it was a result that left them winless in four at home since the win over Barrow on their return to the Environvent Stadium.
Town: Belshaw, Kirby (Kiernan, 45), Burrell, Lawlor, Hall, Thomson, Falkingham, Kerry (Martin, 68) Miller, Beck, Muldoon.
Subs not used: Cracknell, Stead.
Goals: Muldoon (35), Hall (90)
Scunthorpe: Howard, Clarke (Rowe, 78), McGahey, Onariase, Gillead, Loft (Jarvis, 74), Eisa, Spence, Beestin, O'Malley, McAtee (Taylor, 74).
Subs not used: Watson, Bedeau, Green, Hallam, Taylor.
Goals: Onariase (16), Eisa (42, 61 pen), Loft (74), Jarvis (89)