The Wiltshire club needed a point to go up automatically but were pegged back by a resurgent side beaten only once now in 10 League Two starts.
A potential powder-keg was defused by the sympathetic handling of referee Andre Marriner, who lectured players but handed out only one caution.
This came in the fifth minute, when Swindon's Andrew Nicholas collected their 86th yellow card of the season for a clattering challenge near the box.
The passion in his tackle reflected the pressure Rovers built up from the first whistle. A Craig Disley lofted ball gave the Bristol club an early scoring chance but Lambert was off-target.
So was his partner, Richard Walker, when centre-back Steve Elliott minutes later pumped a high ball into the penalty area.
Swindon were getting stuck down in the midfield and their first attempt on goal saw Blair Sturrock only half-connecting with a low cross from Christian Roberts deep on the right.
Both attacks were falling short, Rovers because of a lack of pace to carry them past Jerel Ifil, but the picture changed dramatically in the 27th minute.
Elliott sent yet another ball towards goal, Lambert went between two defenders and from 30 yards fired a volley well out of keeper Phil Smith's reach. It was a stunning goal and it injected life into a rather complacent Swindon.
They were denied an equaliser when Steve Phillips got down well to Michael Pook's shot late in the first half.
Equally, Rovers could point to two first-class saves by Smith, stopping them building on their lead.
Swindon's manager Paul Sturrock took off his son Blair to shift Lee Peacock from the middle line back to his more familiar role in attack.
He also sent on his other two substitutes in an attempt to recover the game, but had to settle for a determined Roberts run into the box, stopped by an equally determined tackle from the impressive Stuart Campbell, and a shot by Pook which was just too high.