Bundee Aki's second-half brace of tries, coupled with a late Jack Carty penalty, steered Connacht to a memorable 28-24 Guinness Pro14 win over Glasgow Warriors at the Sportsground.
Carty finished with 13 points and another of the province's Ireland internationals, Quinn Roux, also touched down as Connacht defeated Scottish opposition for the first time since April 2017.
Glasgow's pressure eventually paid off just before half-time, Adam Hastings slipping Nick Grigg through to make it 7-3 in response to Carty's early penalty.
A run of tries from Aki, Roux, Huw Jones and Aki again produced some exciting exchanges. Tommy Seymour's 70th-minute score made it 25-24, but Connacht held on thanks to a Carty kick with four minutes remaining.
A bruising first half began with Oli Kebble being penalised for side-entry, allowing Carty to open the scoring in the second minute.
Carty and his opposite number Hastings missed penalty attempts after 11 and 20 minutes respectively. The Scotland stand-off's shot came after second row Roux was sin-binned for a no-arms tackle.
Glasgow were looking the more dangerous side, with co-captain Fraser Brown and Jones both gaining good ground, and Aki and Brown both showed their breakdown prowess to win penalties.
Connacht smothered a Glasgow drive in the 32nd minute but they did concede just before the short whistle.
Armed with a penalty advantage, Hastings produced a half-break and short pass to send centre Grigg over.
The increasingly-influential Hastings converted and then added a penalty, five minutes after the restart.
Connacht hit back with Aki's try-scoring burst to the line, which rewarded some fine build-up play from Tom Farrell. Carty converted to make it 10-10
Upping the pace further, Farrell, Alex Wootton and Peter Sullivan stretched the Glasgow defence before Roux crashed in under the posts past Seymour's tackle.
Glasgow quickly got back level at 17-17 when Jones expertly weaved through a midfield gap for Hastings to convert. Carty restored Connacht's lead three minutes later when he punished a Scott Cummings infringement.
Even better followed for the 200 home fans permitted to be at the Sportsground, with John Porch sparking a brilliant break from deep and Wootton's dabbed kick through gleefully dotted down by Aki. Carty missed the touchline conversion.
With an eight-point deficit to overcome, a sweeping Warriors attack ended with Grigg putting Seymour over on the right. Hastings again added the extras, only for Carty's 40-metre penalty to end Connacht's run of six successive defeats to Glasgow.