Stevenage goalkeeper Jamie Jones was tested by Rowan Liburd's header and Garry Thompson's strike from 20 yards.
Boro's Tom Conlon had a shot over the crossbar before Jason McCarthy missed the target and Liburd had more chances.
The winner came from McCarthy's shot rebounding to Luke O'Nien, who slotted home, while Stevenage almost equalised from 10 yards though Dean Parrett.
Stevenage remain in 21st, seven points clear of the relegation zone.

Women's rights activists held a rally outside the parliament building in Warsaw, with more action expected on Monday.
Poland's MPs rejected a near-total ban on abortions on 6 October after mass protests against the move.
But there are new proposals to outlaw abortions in cases where foetuses are unviable or badly damaged.
Jaroslaw Kaczynski, leader of the governing Law and Justice Party (PiS), has said his socially conservative party is working on a new restrictive bill.
In an interview on 12 October (in Polish), he said: "We will strive to ensure that even in pregnancies which are very difficult, when a child is sure to die, strongly deformed, women end up giving birth so that the child can be baptised, buried, and have a name."
Why the outcry over abortion laws in Poland?
The Catholic country already has among the tightest abortion laws in Europe. Currently the procedure is only permitted when there is severe and irreversible damage to the foetus, or a serious threat to the mother's health, or when pregnancy is the result of rape or incest.
The draft law that went before Poland's parliament earlier in October called for women who had abortions to be punished with a five-year prison term. Doctors found to have assisted in an abortion would have also been liable for jail time.
But it was defeated after nationwide "Black Monday" protests that saw tens of thousands of people dressed in black - most of them women - take to the streets.
Women also stayed away from work and school and refused to do domestic chores, in a protest inspired by a women's strike in Iceland in 1975.
Sunday's street protests are expected to continue on Monday, when some women are also planning another strike.
Activists warn that more restrictions on abortion would drive the practice further underground.
Estimates say there are already far more illegal abortions than legal ones in Poland - between 10,000 and 150,000, compared with about 1,000 or 2,000 legal terminations.

The 24-year-old from High Wycombe is chasing his first European Tour victory and a £640,380 winner's cheque.
Hatton's nearest challenger is compatriot Ross Fisher who is three shots back on 14 under par.
"This round is clearly the best round I've ever had," he said.
"I've never actually got to double digits under par before, so I'm very pleased with that.
"The goal now is to get a win. But then it's been a really consistent year, and it would be nice to have a good finish."
Hatton's 10-under 62 at the Old Course - his lowest score on the European Tour - is matched by six other players, including fellow Britons Paul Casey and Tommy Fleetwood.
Sweden's Joakim Lagergren and South Africa's Richard Sterne are four strokes behind on 13 under.
Danny Willett and Lee Westwood - part of Europe's defeated Ryder Cup team in Hazeltine last weekend - are well off the pace on six and 10 over respectively.
However Spaniard Rafael Cabrera-Bello, who took two and a half points from his three matches against the Americans, is better placed on eight under.
Wycombe Wanderers secured a narrow win over Stevenage to move up to eighth and sit one point from the play-off places.
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Polish protesters have launched fresh demonstrations against efforts to further tighten abortion laws.
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England's Tyrrell Hatton will take a three-shot lead into the final round of the Dunhill Links Championship after he equalled the St Andrews Old Course record with a 10-under-par 62.