The visitors arrived bottom of Division One and with their title ambitions long buried but bowled wholeheartedly all day as the Bears reached 283 for four.
Will Rhodes (60, 133 balls) and Dominic Sibley (56, 165) laid a platform for a solid Warwickshire total and Sam Hain (83 not out, 198) and Matt Lamb (44, 92) built on it, but the Bears have work to do in the morning to take the initiative in the title race.
If they reach 350 in 110 overs (for which they need another 67 in 14 overs), then go on to acquire full bowling points and win, they will be champions unless Lancashire (25 for three overnight) total 400 and beat Hampshire at Aigburth. On the first hour today, could the whole title equation hinge!
After putting the Bears in, Somerset bowled well, assisted by some lateral movement and swing, so it was testing work for the batsmen. Rob Yates departed, caught at second slip off Josh Davey, in the fourth over but Sibley and Rhodes concentrated hard to take their side to 80 for one at lunch.
The captain advanced to a compact half-century in 102 balls in the afternoon session and the second-wicket pair added 121 in 41 overs before Rhodes edged Tom Lammonby to wicketkeeper Steven Davies.
Sibley played the shot of the day, a gorgeous down-the-track straight drive off Jack Leach, on the way to passing fifty for the 43rd time in first-class cricket. All day, the ball nipped around though and in the 55th over he copped a perfect outswinger from Jack Brooks which took a nick through to Davies.
That was 139 for three, with the balance of play finely poised, but Hain and Lamb ensured there was no further damage up to tea, at which Warwickshire were 161 for three from 64 overs.
As wickets tumbled at Liverpool, the rising question was how many batting points Warwickshire might need. Hain and Lamb batted watchfully at first, then began to accelerate after tea and added 121 in 41 overs before Brooks trapped Lamb in front.
Michael Burgess, who received his first team cap before play, and Hain batted with freedom to reach the close unbeaten with power to add on day two.