Lennon's side have also reached the Co-operative Insurance Cup final, where they will also face Rangers.
So David Platt's men suffered another major disappointment a week after losing the Co-operative Insurance Cup final in a penalty shoot-out against Glentoran.
Perhaps with one eye on Sunday's Co-operative Insurance Cup, Rangers manager Walter Smith elected to keep Allan McGregor, Naismith and El Hadji Diouf on the bench.
Andy Dorman and Steven Thomson each netted a brace as the Buddies sunk Celtic to banish the painful memories of Sunday's Co-operative Insurance Cup final defeat.
Neil Lennon's side will now meet Aberdeen for a place in the final, having thumped the Dons in the last four of the Co-operative Insurance Cup.
The 62-year-old Smith extended his second hugely-successful spell at Rangers by signing a new one-year contract after retaining the Scottish title and winning the Co-operative Insurance Cup.
However, by then Saints had already knocked Hibernian out of the Co-operative Insurance Cup and claimed another scalp in the next round by ousting near neighbours Dundee United.
Asked if he could give up such trophy-winning occasions with Rangers, Smith preferred to just enjoy the moment after a season when they also lifted the Co-operative Insurance Cup.
Accies manager Billy Reid made six changes to the team that lost 1-0 to Raith in the Co-operative Insurance Cup in midweek as he looked for his first league points.
Jonsson had only been given his starting place because of injury to captain Michael Stewart, who had scored the winner from the penalty spot in the midweek Co-operative Insurance Cup win over Celtic.
The Buddies were looking to recover from their own Old Firm mauling, a 4-0 loss to Celtic, followed by a Co-operative Insurance Cup exit at the hands of First Division side Ross County.
United were taken to extra-time by Ross County in Dingwall in the Co-operative Insurance Cup in midweek and did not return to Dundee, albeit victorious, until the early hours of the following morning.
Both sides will by then have played their opening European fixtures, as will Falkirk and Motherwell, while St Johnstone and St Mirren will have played in the first round of the Co-operative Insurance Cup.
Neil Alexander started in goal in place of regular first choice Allan McGregor with the former expected to feature in this month's Co-operative Insurance Cup final against Celtic, as is customary for that competition.
McInnes freshened up his side after the midweek Co-operative Insurance Cup defeat, Jennison Myrie-Williams coming in for the injured Murray Davidson, while Marcus Haber, Peter MacDonald and Steven Milne came in for Collin Samuel, Sam Parkin and Andy Jackson.
BBC: Saints boss McInnes unhappy with basic defensive errors
Rangers were coming off the back of their midweek Co-operative Insurance Cup success, although Walter Smith freshened up his side by introducing Steven Whittaker and John Fleck for Sasa Papac and Steven Naismith after their semi-final victory over Falkirk.
Strachan, winning the Manager of the Year award for the second time, has led Celtic to the Co-operative Insurance Cup this season and his team are a point ahead of rivals Rangers at the top of the Premier League.
Livi travel to Coatbridge on Saturday in the first round of the Co-operative Insurance Cup and Rovers manager Martin believes the footballing authorities must pay closer scrutiny to the books as clubs continue to shell out cash they do not have.
Those players, and the management team of Smith, Ally McCoist and Kenny McDowall, have contributed to the club's success to date in the current campaign, with the Co-operative Insurance Cup in the trophy room and three wins required to retain the Scottish Premier League.
The Co-operative Insurance company apply their name to the League Cup for the last time this Sabbath, and in the wake of the Old Firm final, Scottish football will have two of its three major competitions without financial backers.
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